Subgroups — C₅×#17764 #11940484

Order 1280.

964 conjugacy classes of subgroups.

The subgroup lattice has 528 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#3511	C₂	1	1	yes	maximal, characteristic
2	C₅×#2989	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#2906	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#1560	C₂	1	2	yes	maximal, complemented
5	C₅×#1559	C₂	1	2	yes	maximal, complemented
6	C₅×#1551	C₂	1	2	yes	maximal, complemented
7	C₅×#1550	C₂	1	2	yes	maximal, complemented
8	C₅×#1548	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#1547	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₅×#333	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#1540	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₅×#131	—	2	1	no	—
13	C₅×#556	C₄	1	2	yes	—
14	C₅×#555	—	2	1	no	—
15	C₅×#554	—	2	1	no	—
16	C₅×#553	—	2	2	no	—
17	C₅×#548	C₄	1	4	yes	—
18	C₅×#547	C₄	1	2	yes	—
19	C₅×#542	—	2	2	no	—
20	C₅×#537	—	2	1	no	—
21	C₅×#533	C₂²	1	2	yes	—
22	C₅×#532	C₂²	1	2	yes	—
23	C₅×#532	C₂²	1	1	yes	characteristic
24	C₂×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
25	C₅×#520	—	2	1	no	—
26	C₄×C₅×#41	C₂²	1	1	yes	characteristic
27	C₅×#446	—	2	1	no	—
28	C₅×#436	—	2	1	no	—
29	C₅×#435	—	2	2	no	—
30	C₅×#432	C₂²	1	2	yes	—
31	C₅×#431	C₂²	1	1	yes	characteristic
32	C₅×#424	—	2	1	no	—
33	C₅×#424	—	2	2	no	—
34	C₅×#423	C₂²	1	2	yes	—
35	C₅×#423	C₂²	1	1	yes	characteristic
36	C₅×#423	C₂²	1	2	yes	—
37	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
38	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
39	C₂×C₅×C₄⋊C₈	C₂²	1	2	yes	—
40	C₅×#333	C₂²	1	2	yes	—
41	C₅×#333	C₂²	1	2	yes	—
42	C₅×#333	C₂²	1	2	yes	—
43	C₅×#333	C₂²	1	2	yes	—
44	C₅×#332	C₂²	1	1	yes	characteristic
45	C₅×#332	C₂²	1	1	yes	characteristic
46	C₅×#332	C₂²	1	2	yes	—
47	C₅×#331	C₂²	1	1	yes	characteristic
48	C₅×#331	C₂²	1	1	yes	characteristic
49	C₅×#331	C₂²	1	2	yes	—
50	#17764	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
51	C₂×C₅×#41	—	2	1	no	—
52	C₂×C₅×#41	C₂×C₄	1	4	yes	—
53	C₂×C₅×#41	D₄	1	1	yes	characteristic
54	C₂²×C₅×Q₈	C₂×C₄	1	2	yes	—
55	C₅×#131	—	4	4	no	—
56	C₂×C₅×M₁₆	—	2	2	no	—
57	C₂×C₅×M₁₆	—	2	1	no	—
58	C₂×C₅×M₁₆	—	2	2	no	—
59	C₂²×C₅×C₈	—	2	2	no	—
60	C₂²×C₅×C₈	—	2	1	no	—
61	C₂²×C₅×C₈	—	2	1	no	—
62	C₅×C₄⋊Q₈	—	2	1	no	—
63	C₅×C₄⋊Q₈	—	2	1	no	—
64	C₅×C₄⋊Q₈	C₂×C₄	1	2	yes	—
65	C₅×C₄⋊Q₈	C₂³	1	2	yes	—
66	C₅×C₄⋊Q₈	C₂³	1	1	yes	characteristic
67	C₅×#127	C₂³	1	1	yes	characteristic
68	C₅×#126	—	2	4	no	—
69	C₅×#125	—	2	2	no	—
70	C₅×#124	—	2	4	no	—
71	C₅×#124	—	2	1	no	—
72	C₅×#124	C₂×C₄	1	4	yes	—
73	C₅×#123	—	2	4	no	—
74	C₅×C₂²⋊Q₈	—	2	2	no	—
75	C₅×C₂²⋊Q₈	—	2	2	no	—
76	C₅×C₂²⋊Q₈	—	2	4	no	—
77	C₅×C₂²⋊Q₈	C₂×C₄	1	4	yes	—
78	C₅×#121	—	2	2	no	—
79	C₅×#121	—	2	4	no	—
80	C₅×#121	—	2	2	no	—
81	C₅×#121	—	2	1	no	—
82	C₅×#121	—	2	2	no	—
83	C₅×#121	C₂×C₄	1	2	yes	—
84	C₄×C₅×Q₈	—	2	2	no	—
85	C₄×C₅×Q₈	C₂×C₄	1	4	yes	—
86	C₄×C₅×Q₈	C₂×C₄	1	1	yes	characteristic
87	C₄×C₅×Q₈	D₄	1	1	yes	characteristic
88	C₄×C₅×D₄	—	2	4	no	—
89	C₄×C₅×D₄	—	2	2	no	—
90	C₄×C₅×D₄	—	2	2	no	—
91	C₄×C₅×D₄	—	2	1	no	—
92	C₄×C₅×D₄	C₂×C₄	1	2	yes	—
93	C₄×C₅×D₄	C₂×C₄	1	1	yes	characteristic
94	C₄×C₅×D₄	C₂×C₄	1	2	yes	—
95	C₄×C₅×D₄	D₄	1	2	yes	—
96	C₄×C₅×D₄	D₄	1	1	yes	characteristic
97	C₅×#117	—	2	2	no	—
98	C₅×#117	—	2	2	no	—
99	C₅×#117	D₄	1	1	yes	characteristic
100	C₅×#117	D₄	1	2	yes	—
101	C₂×C₅×C₄⋊C₄	—	2	1	no	—
102	C₂×C₅×C₄⋊C₄	—	2	1	no	—
103	C₂×C₅×C₄⋊C₄	—	2	2	no	—
104	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
105	C₂×C₄²×C₅	C₂³	1	2	yes	—
106	C₅×C₄⋊C₈	—	2	2	no	—
107	C₅×C₄⋊C₈	—	2	1	no	—
108	C₅×C₄⋊C₈	—	2	1	no	—
109	C₅×C₄⋊C₈	—	2	2	no	—
110	C₅×C₄⋊C₈	—	2	1	no	—
111	C₅×C₄⋊C₈	—	2	2	no	—
112	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
113	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
114	C₅×C₄⋊C₈	C₂³	1	2	yes	—
115	C₅×C₄⋊C₈	C₂³	1	2	yes	—
116	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
117	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
118	C₅×C₂²⋊C₈	—	2	1	no	—
119	C₅×C₂²⋊C₈	—	2	2	no	—
120	C₅×#97	—	2	2	no	—
121	C₄×C₅×C₈	—	2	1	no	—
122	#3511	C₂×C₅	1	1	yes	characteristic
123	#2989	C₂×C₅	1	1	yes	characteristic, complemented
124	#2906	C₂×C₅	1	1	yes	characteristic, complemented
125	#1560	C₂×C₅	1	2	yes	complemented
126	#1559	C₂×C₅	1	2	yes	complemented
127	#1551	C₂×C₅	1	2	yes	complemented
128	#1550	C₂×C₅	1	2	yes	complemented
129	#1548	C₂×C₅	1	1	yes	characteristic, complemented
130	#1547	C₂×C₅	1	1	yes	characteristic, complemented
131	C₂×#333	C₂×C₅	1	1	yes	characteristic, complemented
132	#1540	C₂×C₅	1	1	yes	characteristic, complemented
133	C₅×#41	—	2	2	no	—
134	C₅×#41	—	2	2	no	—
135	C₅×#41	—	4	2	no	—
136	C₅×#41	—	4	2	no	—
137	C₅×#41	—	8	4	no	—
138	C₂×C₅×Q₈	—	2	2	no	—
139	C₂×C₅×Q₈	—	2	1	no	—
140	C₂×C₅×Q₈	—	8	2	no	—
141	C₂×C₅×Q₈	C₂²⋊C₄	1	1	yes	characteristic
142	C₂×C₅×Q₈	C₂²×C₄	1	4	yes	—
143	C₂×C₅×D₄	—	2	2	no	—
144	C₂×C₅×D₄	—	2	4	no	—
145	C₂×C₅×D₄	—	2	1	no	—
146	C₂×C₅×D₄	—	2	1	no	—
147	C₂×C₅×D₄	C₂²⋊C₄	1	2	yes	—
148	C₂×C₅×D₄	C₂²⋊C₄	1	1	yes	characteristic
149	C₂×C₅×D₄	C₂²×C₄	1	2	yes	—
150	C₂²×C₄×C₅	—	2	2	no	—
151	C₂²×C₄×C₅	—	2	2	no	—
152	C₂²×C₄×C₅	—	2	4	no	—
153	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
154	C₂²×C₄×C₅	C₂²×C₄	1	2	yes	—
155	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
156	C₂²×C₄×C₅	C₂×D₄	1	2	yes	—
157	C₂²×C₄×C₅	C₂×D₄	1	2	yes	—
158	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
159	C₅×M₁₆	—	4	4	no	—
160	C₅×M₁₆	—	4	2	no	—
161	C₅×M₁₆	—	8	2	no	—
162	C₂×C₅×C₈	—	2	1	no	—
163	C₂×C₅×C₈	—	2	2	no	—
164	C₂×C₅×C₈	—	2	1	no	—
165	C₂×C₅×C₈	—	2	2	no	—
166	C₂×C₅×C₈	—	2	1	no	—
167	C₂×C₅×C₈	—	2	1	no	—
168	C₂×C₅×C₈	—	4	4	no	—
169	C₂×C₅×C₈	—	4	2	no	—
170	C₂×C₅×C₈	—	8	1	no	—
171	C₅×C₄⋊C₄	—	2	2	no	—
172	C₅×C₄⋊C₄	—	2	4	no	—
173	C₅×C₄⋊C₄	—	2	2	no	—
174	C₅×C₄⋊C₄	—	2	4	no	—
175	C₅×C₄⋊C₄	—	2	2	no	—
176	C₅×C₄⋊C₄	—	2	2	no	—
177	C₅×C₄⋊C₄	—	2	1	no	—
178	C₅×C₄⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
179	C₅×C₄⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
180	C₅×C₄⋊C₄	C₂²⋊C₄	1	2	yes	—
181	C₅×C₄⋊C₄	C₂²⋊C₄	1	2	yes	—
182	C₅×C₄⋊C₄	C₂²×C₄	1	2	yes	—
183	C₅×C₂²⋊C₄	—	2	4	no	—
184	C₅×C₂²⋊C₄	—	2	4	no	—
185	C₅×C₂²⋊C₄	—	2	4	no	—
186	C₅×C₂²⋊C₄	—	2	2	no	—
187	C₅×C₂²⋊C₄	—	2	2	no	—
188	C₅×C₂²⋊C₄	C₂²⋊C₄	1	2	yes	—
189	C₅×C₂²⋊C₄	C₂²⋊C₄	1	2	yes	—
190	C₅×C₂²⋊C₄	C₂²⋊C₄	1	2	yes	—
191	C₄²×C₅	—	2	4	no	—
192	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
193	C₄²×C₅	C₂²×C₄	1	2	yes	—
194	C₄²×C₅	C₂×D₄	1	2	yes	—
195	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
196	C₄²×C₅	C₂×D₄	1	2	yes	—
197	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
198	C₄²×C₅	C₂⁴	1	1	yes	characteristic
199	C₂×#131	—	2	1	no	—
200	#556	C₄×C₅	1	2	yes	—
201	#555	—	2	1	no	—
202	#554	—	2	1	no	—
203	#553	—	2	2	no	—
204	#548	C₄×C₅	1	4	yes	—
205	#547	C₄×C₅	1	2	yes	—
206	#542	—	2	2	no	—
207	#537	—	2	1	no	—
208	#533	C₂²×C₅	1	2	yes	—
209	#532	C₂²×C₅	1	2	yes	—
210	#532	C₂²×C₅	1	1	yes	characteristic
211	C₂×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
212	#520	—	2	1	no	—
213	C₄×#41	C₂²×C₅	1	1	yes	characteristic
214	#446	—	2	1	no	—
215	#436	—	2	1	no	—
216	#435	—	2	2	no	—
217	#432	C₂²×C₅	1	2	yes	—
218	#431	C₂²×C₅	1	1	yes	characteristic
219	#424	—	2	1	no	—
220	#424	—	2	2	no	—
221	#423	C₂²×C₅	1	1	yes	characteristic
222	#423	C₂²×C₅	1	2	yes	—
223	#423	C₂²×C₅	1	2	yes	—
224	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
225	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
226	C₂×C₄⋊C₈	C₂²×C₅	1	2	yes	—
227	#333	C₂²×C₅	1	2	yes	—
228	#333	C₂²×C₅	1	2	yes	—
229	#333	C₂²×C₅	1	2	yes	—
230	#333	C₂²×C₅	1	2	yes	—
231	#332	C₂²×C₅	1	1	yes	characteristic
232	#332	C₂²×C₅	1	1	yes	characteristic
233	#332	C₂²×C₅	1	2	yes	—
234	#331	C₂²×C₅	1	1	yes	characteristic
235	#331	C₂²×C₅	1	1	yes	characteristic
236	#331	C₂²×C₅	1	2	yes	—
237	C₂³×C₅	—	2	2	no	—
238	C₂³×C₅	C₂×C₂²⋊C₄	1	2	yes	—
239	C₂³×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
240	C₅×Q₈	—	2	2	no	—
241	C₅×Q₈	—	4	4	no	—
242	C₅×Q₈	—	4	1	no	—
243	C₅×Q₈	—	4	1	no	—
244	C₅×Q₈	—	8	2	no	—
245	C₅×D₄	—	2	4	no	—
246	C₅×D₄	—	2	2	no	—
247	C₅×D₄	—	4	2	no	—
248	C₅×D₄	—	4	4	no	—
249	C₅×D₄	—	4	1	no	—
250	C₅×D₄	—	4	1	no	—
251	C₅×D₄	—	4	1	no	—
252	C₅×D₄	—	4	1	no	—
253	C₅×D₄	—	8	4	no	—
254	C₂×C₄×C₅	—	2	2	no	—
255	C₂×C₄×C₅	—	2	2	no	—
256	C₂×C₄×C₅	—	2	1	no	—
257	C₂×C₄×C₅	—	2	2	no	—
258	C₂×C₄×C₅	—	2	1	no	—
259	C₂×C₄×C₅	—	2	2	no	—
260	C₂×C₄×C₅	—	2	2	no	—
261	C₂×C₄×C₅	—	2	4	no	—
262	C₂×C₄×C₅	—	4	1	no	—
263	C₂×C₄×C₅	—	4	2	no	—
264	C₂×C₄×C₅	—	4	4	no	—
265	C₂×C₄×C₅	—	8	4	no	—
266	C₂×C₄×C₅	—	8	2	no	—
267	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	2	yes	—
268	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
269	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	2	yes	—
270	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
271	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	2	yes	—
272	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
273	C₂×C₄×C₅	AGL(1,ℤ/8)	1	2	yes	—
274	C₂×C₄×C₅	#137	1	2	yes	—
275	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
276	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
277	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
278	C₅×C₈	—	4	1	no	—
279	C₅×C₈	—	4	2	no	—
280	C₅×C₈	—	4	1	no	—
281	C₅×C₈	—	4	2	no	—
282	C₅×C₈	—	4	1	no	—
283	C₅×C₈	—	4	1	no	—
284	C₂×#41	—	2	1	no	—
285	C₂×#41	C₂×C₄×C₅	1	4	yes	—
286	C₂×#41	C₅×D₄	1	1	yes	characteristic
287	C₂²×Q₈	C₂×C₄×C₅	1	2	yes	—
288	#131	—	4	4	no	—
289	C₂×M₁₆	—	2	2	no	—
290	C₂×M₁₆	—	2	1	no	—
291	C₂×M₁₆	—	2	2	no	—
292	C₂²×C₈	—	2	2	no	—
293	C₂²×C₈	—	2	1	no	—
294	C₂²×C₈	—	2	1	no	—
295	C₄⋊Q₈	—	2	1	no	—
296	C₄⋊Q₈	—	2	1	no	—
297	C₄⋊Q₈	C₂×C₄×C₅	1	2	yes	—
298	C₄⋊Q₈	C₂³×C₅	1	2	yes	—
299	C₄⋊Q₈	C₂³×C₅	1	1	yes	characteristic
300	#127	C₂³×C₅	1	1	yes	characteristic
301	#126	—	2	4	no	—
302	#125	—	2	2	no	—
303	#124	—	2	4	no	—
304	#124	—	2	1	no	—
305	#124	C₂×C₄×C₅	1	4	yes	—
306	#123	—	2	4	no	—
307	C₂²⋊Q₈	—	2	2	no	—
308	C₂²⋊Q₈	—	2	2	no	—
309	C₂²⋊Q₈	—	2	4	no	—
310	C₂²⋊Q₈	C₂×C₄×C₅	1	4	yes	—
311	#121	—	2	2	no	—
312	#121	—	2	4	no	—
313	#121	—	2	2	no	—
314	#121	—	2	1	no	—
315	#121	—	2	2	no	—
316	#121	C₂×C₄×C₅	1	2	yes	—
317	C₄×Q₈	—	2	2	no	—
318	C₄×Q₈	C₂×C₄×C₅	1	4	yes	—
319	C₄×Q₈	C₂×C₄×C₅	1	1	yes	characteristic
320	C₄×Q₈	C₅×D₄	1	1	yes	characteristic
321	C₄×D₄	—	2	4	no	—
322	C₄×D₄	—	2	2	no	—
323	C₄×D₄	—	2	2	no	—
324	C₄×D₄	—	2	1	no	—
325	C₄×D₄	C₂×C₄×C₅	1	2	yes	—
326	C₄×D₄	C₂×C₄×C₅	1	1	yes	characteristic
327	C₄×D₄	C₂×C₄×C₅	1	2	yes	—
328	C₄×D₄	C₅×D₄	1	2	yes	—
329	C₄×D₄	C₅×D₄	1	1	yes	characteristic
330	#117	—	2	2	no	—
331	#117	—	2	2	no	—
332	#117	C₅×D₄	1	1	yes	characteristic
333	#117	C₅×D₄	1	2	yes	—
334	C₂×C₄⋊C₄	—	2	1	no	—
335	C₂×C₄⋊C₄	—	2	1	no	—
336	C₂×C₄⋊C₄	—	2	2	no	—
337	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
338	C₂×C₄²	C₂³×C₅	1	2	yes	—
339	C₄⋊C₈	—	2	2	no	—
340	C₄⋊C₈	—	2	1	no	—
341	C₄⋊C₈	—	2	1	no	—
342	C₄⋊C₈	—	2	2	no	—
343	C₄⋊C₈	—	2	1	no	—
344	C₄⋊C₈	—	2	2	no	—
345	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
346	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
347	C₄⋊C₈	C₂³×C₅	1	2	yes	—
348	C₄⋊C₈	C₂³×C₅	1	2	yes	—
349	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
350	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
351	C₂²⋊C₈	—	2	1	no	—
352	C₂²⋊C₈	—	2	2	no	—
353	#97	—	2	2	no	—
354	C₄×C₈	—	2	1	no	—
355	C₂²×C₅	—	2	1	no	—
356	C₂²×C₅	—	2	1	no	—
357	C₂²×C₅	—	2	2	no	—
358	C₂²×C₅	—	2	2	no	—
359	C₂²×C₅	—	2	2	no	—
360	C₂²×C₅	—	4	2	no	—
361	C₂²×C₅	—	4	2	no	—
362	C₂²×C₅	—	4	2	no	—
363	C₂²×C₅	#417	1	2	yes	—
364	C₂²×C₅	C₂²×C₂²⋊C₄	1	1	yes	characteristic
365	C₄×C₅	—	2	1	no	—
366	C₄×C₅	—	2	2	no	—
367	C₄×C₅	—	2	1	no	—
368	C₄×C₅	—	2	2	no	—
369	C₄×C₅	—	2	1	no	—
370	C₄×C₅	—	2	2	no	—
371	C₄×C₅	—	4	4	no	—
372	C₄×C₅	—	4	2	no	—
373	C₄×C₅	#417	1	2	yes	—
374	C₄×C₅	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
375	C₄×C₅	C₂×#137	1	1	yes	characteristic
376	C₄×C₅	#577	1	1	yes	characteristic
377	C₄×C₅	#578	1	1	yes	characteristic
378	#41	—	2	2	no	—
379	#41	—	2	2	no	—
380	#41	—	4	2	no	—
381	#41	—	4	2	no	—
382	#41	—	8	4	no	—
383	C₂×Q₈	—	2	2	no	—
384	C₂×Q₈	—	2	1	no	—
385	C₂×Q₈	—	8	2	no	—
386	C₂×Q₈	C₅×C₂²⋊C₄	1	1	yes	characteristic
387	C₂×Q₈	C₂²×C₄×C₅	1	4	yes	—
388	C₂×D₄	—	2	2	no	—
389	C₂×D₄	—	2	4	no	—
390	C₂×D₄	—	2	1	no	—
391	C₂×D₄	—	2	1	no	—
392	C₂×D₄	C₅×C₂²⋊C₄	1	2	yes	—
393	C₂×D₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
394	C₂×D₄	C₂²×C₄×C₅	1	2	yes	—
395	C₂²×C₄	—	2	2	no	—
396	C₂²×C₄	—	2	2	no	—
397	C₂²×C₄	—	2	4	no	—
398	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
399	C₂²×C₄	C₂²×C₄×C₅	1	2	yes	—
400	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
401	C₂²×C₄	C₂×C₅×D₄	1	2	yes	—
402	C₂²×C₄	C₂×C₅×D₄	1	2	yes	—
403	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
404	M₁₆	—	4	4	no	—
405	M₁₆	—	4	2	no	—
406	M₁₆	—	8	2	no	—
407	C₂×C₈	—	2	1	no	—
408	C₂×C₈	—	2	1	no	—
409	C₂×C₈	—	2	2	no	—
410	C₂×C₈	—	2	1	no	—
411	C₂×C₈	—	2	2	no	—
412	C₂×C₈	—	2	1	no	—
413	C₂×C₈	—	4	4	no	—
414	C₂×C₈	—	4	2	no	—
415	C₂×C₈	—	8	1	no	—
416	C₄⋊C₄	—	2	2	no	—
417	C₄⋊C₄	—	2	4	no	—
418	C₄⋊C₄	—	2	2	no	—
419	C₄⋊C₄	—	2	4	no	—
420	C₄⋊C₄	—	2	2	no	—
421	C₄⋊C₄	—	2	2	no	—
422	C₄⋊C₄	—	2	1	no	—
423	C₄⋊C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
424	C₄⋊C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
425	C₄⋊C₄	C₅×C₂²⋊C₄	1	2	yes	—
426	C₄⋊C₄	C₅×C₂²⋊C₄	1	2	yes	—
427	C₄⋊C₄	C₂²×C₄×C₅	1	2	yes	—
428	C₂²⋊C₄	—	2	4	no	—
429	C₂²⋊C₄	—	2	4	no	—
430	C₂²⋊C₄	—	2	4	no	—
431	C₂²⋊C₄	—	2	2	no	—
432	C₂²⋊C₄	—	2	2	no	—
433	C₂²⋊C₄	C₅×C₂²⋊C₄	1	2	yes	—
434	C₂²⋊C₄	C₅×C₂²⋊C₄	1	2	yes	—
435	C₂²⋊C₄	C₅×C₂²⋊C₄	1	2	yes	—
436	C₄²	—	2	4	no	—
437	C₄²	C₂²×C₄×C₅	1	1	yes	characteristic
438	C₄²	C₂²×C₄×C₅	1	2	yes	—
439	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
440	C₄²	C₂×C₅×D₄	1	2	yes	—
441	C₄²	C₂×C₅×D₄	1	2	yes	—
442	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
443	C₄²	C₂⁴×C₅	1	1	yes	characteristic
444	C₂×C₅	—	2	2	no	—
445	C₂×C₅	—	4	2	no	—
446	C₂×C₅	—	8	2	no	—
447	C₂×C₅	#2888	1	1	yes	characteristic
448	C₂×C₅	C₂×#417	1	1	yes	characteristic
449	C₂×C₅	#2898	1	1	yes	characteristic
450	C₂³	—	2	2	no	—
451	C₂³	C₂×C₅×C₂²⋊C₄	1	2	yes	—
452	C₂³	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
453	Q₈	—	2	2	no	—
454	Q₈	—	4	4	no	—
455	Q₈	—	4	1	no	—
456	Q₈	—	4	1	no	—
457	Q₈	—	8	2	no	—
458	D₄	—	2	4	no	—
459	D₄	—	2	2	no	—
460	D₄	—	4	2	no	—
461	D₄	—	4	4	no	—
462	D₄	—	4	1	no	—
463	D₄	—	4	1	no	—
464	D₄	—	4	1	no	—
465	D₄	—	4	1	no	—
466	D₄	—	8	4	no	—
467	C₂×C₄	—	2	2	no	—
468	C₂×C₄	—	2	2	no	—
469	C₂×C₄	—	2	1	no	—
470	C₂×C₄	—	2	2	no	—
471	C₂×C₄	—	2	1	no	—
472	C₂×C₄	—	2	2	no	—
473	C₂×C₄	—	2	2	no	—
474	C₂×C₄	—	2	4	no	—
475	C₂×C₄	—	4	1	no	—
476	C₂×C₄	—	4	2	no	—
477	C₂×C₄	—	4	4	no	—
478	C₂×C₄	—	8	4	no	—
479	C₂×C₄	—	8	2	no	—
480	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	2	yes	—
481	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
482	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	2	yes	—
483	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
484	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	2	yes	—
485	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
486	C₂×C₄	C₅×AGL(1,ℤ/8)	1	2	yes	—
487	C₂×C₄	C₅×#137	1	2	yes	—
488	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
489	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
490	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
491	C₈	—	4	1	no	—
492	C₈	—	4	2	no	—
493	C₈	—	4	1	no	—
494	C₈	—	4	2	no	—
495	C₈	—	4	1	no	—
496	C₈	—	4	1	no	—
497	C₅	#17764	1	1	yes	characteristic, direct product factor, Sylow
498	C₂²	—	2	1	no	—
499	C₂²	—	2	1	no	—
500	C₂²	—	2	2	no	—
501	C₂²	—	2	2	no	—
502	C₂²	—	2	2	no	—
503	C₂²	—	4	2	no	—
504	C₂²	—	4	2	no	—
505	C₂²	—	4	2	no	—
506	C₂²	C₅×#417	1	2	yes	—
507	C₂²	C₂²×C₅×C₂²⋊C₄	1	1	yes	characteristic
508	C₄	—	2	1	no	—
509	C₄	—	2	2	no	—
510	C₄	—	2	1	no	—
511	C₄	—	2	2	no	—
512	C₄	—	2	1	no	—
513	C₄	—	2	2	no	—
514	C₄	—	4	4	no	—
515	C₄	—	4	2	no	—
516	C₄	C₅×#417	1	2	yes	—
517	C₄	C₂×C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
518	C₄	C₂×C₅×#137	1	1	yes	characteristic
519	C₄	C₅×#577	1	1	yes	characteristic
520	C₄	C₅×#578	1	1	yes	characteristic
521	C₂	—	2	2	no	—
522	C₂	—	4	2	no	—
523	C₂	—	8	2	no	—
524	C₂	C₅×#2888	1	1	yes	characteristic
525	C₂	C₂×C₅×#417	1	1	yes	characteristic
526	C₂	C₅×#2898	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₅	C₂²×C₂²⋊C₄
commutator	C₂×C₄	C₂³×C₄×C₅
Frattini, cosocle	C₄²	C₂⁴×C₅
prime radical	C₅×#3511	C₂
LCS	G ▷ C₂×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₅ ◁ C₄×C₅×#41 ◁ G

Complements

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

N	H ≅ G/N	type
2. C₅×#2989	C₂	semidirect
3. C₅×#2906	C₂	semidirect
4. C₅×#1560	C₂	semidirect
5. C₅×#1559	C₂	semidirect
6. C₅×#1551	C₂	semidirect
7. C₅×#1550	C₂	semidirect
8. C₅×#1548	C₂	semidirect
9. C₅×#1547	C₂	semidirect
10. C₂×C₅×#333	C₂	semidirect
11. C₅×#1540	C₂	semidirect
50. #17764	C₅	direct (N × H)
123. #2989	C₂×C₅	semidirect
124. #2906	C₂×C₅	semidirect
125. #1560	C₂×C₅	semidirect
126. #1559	C₂×C₅	semidirect
127. #1551	C₂×C₅	semidirect
128. #1550	C₂×C₅	semidirect
129. #1548	C₂×C₅	semidirect
130. #1547	C₂×C₅	semidirect
131. C₂×#333	C₂×C₅	semidirect
132. #1540	C₂×C₅	semidirect
497. C₅	#17764	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×#3511	2
C₅×#2989	2
C₅×#2906	2
C₅×#1560	2
C₅×#1559	2
C₅×#1551	2
C₅×#1550	2
C₅×#1548	2
C₅×#1547	2
C₂×C₅×#333	2
C₅×#1540	2
#17764	5

Subgroups — C5×#17764 #11940484

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#17764 #11940484