Subgroups — C₅×#17763 #11940483

Order 1280.

908 conjugacy classes of subgroups.

The subgroup lattice has 504 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#3509	C₂	1	1	yes	maximal, characteristic
2	C₅×#2989	C₂	1	1	yes	maximal, characteristic
3	C₅×#2906	C₂	1	1	yes	maximal, characteristic
4	C₅×#1561	C₂	1	2	yes	maximal, complemented
5	C₅×#1559	C₂	1	2	yes	maximal, complemented
6	C₅×#1552	C₂	1	2	yes	maximal, complemented
7	C₅×#1550	C₂	1	2	yes	maximal, complemented
8	C₅×#1550	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#1546	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#1542	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₅×#332	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₅×#131	—	2	1	no	—
13	C₅×#557	—	2	1	no	—
14	C₅×#557	C₄	1	2	yes	—
15	C₅×#556	—	2	1	no	—
16	C₅×#556	C₄	1	2	yes	—
17	C₅×#552	—	2	2	no	—
18	C₅×#552	C₄	1	4	yes	—
19	C₅×#541	—	2	2	no	—
20	C₅×#536	—	2	1	no	—
21	C₅×#533	C₂²	1	1	yes	characteristic
22	C₅×#533	C₂²	1	2	yes	—
23	C₅×#533	C₂²	1	2	yes	—
24	C₂×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
25	C₅×#519	—	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	1	yes	characteristic
41	C₅×#333	C₂²	1	1	yes	characteristic
42	C₅×#333	C₂²	1	2	yes	—
43	C₅×#332	C₂²	1	2	yes	—
44	C₅×#332	C₂²	1	2	yes	—
45	C₅×#332	C₂²	1	1	yes	characteristic
46	C₅×#332	C₂²	1	1	yes	characteristic
47	C₅×#332	C₂²	1	2	yes	—
48	C₅×#332	C₂²	1	2	yes	—
49	C₅×#332	C₂²	1	2	yes	—
50	#17763	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
51	C₂×C₅×#41	D₄	1	1	yes	characteristic
52	C₂²×C₅×Q₈	—	2	1	no	—
53	C₅×#131	—	4	4	no	—
54	C₂×C₅×M₁₆	—	2	2	no	—
55	C₂×C₅×M₁₆	—	2	1	no	—
56	C₂×C₅×M₁₆	—	2	2	no	—
57	C₂²×C₅×C₈	—	2	2	no	—
58	C₂²×C₅×C₈	—	2	1	no	—
59	C₂²×C₅×C₈	—	2	1	no	—
60	C₅×C₄⋊Q₈	—	2	2	no	—
61	C₅×C₄⋊Q₈	—	2	1	no	—
62	C₅×C₄⋊Q₈	—	2	1	no	—
63	C₅×C₄⋊Q₈	C₂×C₄	1	2	yes	—
64	C₅×C₄⋊Q₈	C₂³	1	1	yes	characteristic
65	C₅×C₄⋊Q₈	C₂³	1	2	yes	—
66	C₅×C₄⋊Q₈	C₂³	1	1	yes	characteristic
67	C₅×#126	—	2	4	no	—
68	C₅×#126	—	2	4	no	—
69	C₅×#125	—	2	4	no	—
70	C₅×#125	—	2	4	no	—
71	C₅×#125	—	2	1	no	—
72	C₅×#125	—	2	2	no	—
73	C₅×#125	C₂×C₄	1	4	yes	—
74	C₅×#124	—	2	2	no	—
75	C₅×#123	—	2	4	no	—
76	C₅×C₂²⋊Q₈	—	2	2	no	—
77	C₅×C₂²⋊Q₈	—	2	2	no	—
78	C₅×C₂²⋊Q₈	—	2	1	no	—
79	C₅×C₂²⋊Q₈	—	2	2	no	—
80	C₅×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
81	C₅×C₂²⋊Q₈	C₂×C₄	1	4	yes	—
82	C₄×C₅×Q₈	—	2	2	no	—
83	C₄×C₅×Q₈	—	2	2	no	—
84	C₄×C₅×Q₈	—	2	2	no	—
85	C₄×C₅×Q₈	—	2	2	no	—
86	C₄×C₅×Q₈	—	2	2	no	—
87	C₄×C₅×Q₈	—	2	1	no	—
88	C₄×C₅×Q₈	C₂×C₄	1	4	yes	—
89	C₄×C₅×Q₈	C₂×C₄	1	2	yes	—
90	C₄×C₅×Q₈	C₂×C₄	1	1	yes	characteristic
91	C₄×C₅×Q₈	D₄	1	1	yes	characteristic
92	C₄×C₅×D₄	C₂×C₄	1	2	yes	—
93	C₄×C₅×D₄	C₂×C₄	1	1	yes	characteristic
94	C₄×C₅×D₄	D₄	1	2	yes	—
95	C₄×C₅×D₄	D₄	1	1	yes	characteristic
96	C₅×#117	—	2	1	no	—
97	C₅×#117	—	2	2	no	—
98	C₅×#117	—	2	4	no	—
99	C₅×#117	C₂×C₄	1	4	yes	—
100	C₅×#117	D₄	1	1	yes	characteristic
101	C₅×#117	D₄	1	2	yes	—
102	C₂×C₅×C₄⋊C₄	—	2	1	no	—
103	C₂×C₅×C₄⋊C₄	C₂×C₄	1	2	yes	—
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	#3509	C₂×C₅	1	1	yes	characteristic
123	#2989	C₂×C₅	1	1	yes	characteristic
124	#2906	C₂×C₅	1	1	yes	characteristic
125	#1561	C₂×C₅	1	2	yes	complemented
126	#1559	C₂×C₅	1	2	yes	complemented
127	#1552	C₂×C₅	1	2	yes	complemented
128	#1550	C₂×C₅	1	1	yes	characteristic, complemented
129	#1550	C₂×C₅	1	2	yes	complemented
130	#1546	C₂×C₅	1	1	yes	characteristic, complemented
131	#1542	C₂×C₅	1	1	yes	characteristic, complemented
132	C₂×#332	C₂×C₅	1	1	yes	characteristic, complemented
133	C₅×#41	—	2	2	no	—
134	C₅×#41	—	2	2	no	—
135	C₂×C₅×Q₈	—	2	2	no	—
136	C₂×C₅×Q₈	—	2	1	no	—
137	C₂×C₅×Q₈	—	2	2	no	—
138	C₂×C₅×Q₈	—	4	2	no	—
139	C₂×C₅×Q₈	—	4	2	no	—
140	C₂×C₅×Q₈	C₂²⋊C₄	1	1	yes	characteristic
141	C₂×C₅×Q₈	C₂²×C₄	1	2	yes	—
142	C₂×C₅×D₄	C₂²⋊C₄	1	2	yes	—
143	C₂×C₅×D₄	C₂²⋊C₄	1	1	yes	characteristic
144	C₂²×C₄×C₅	—	2	2	no	—
145	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
146	C₂²×C₄×C₅	C₂²×C₄	1	2	yes	—
147	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
148	C₂²×C₄×C₅	C₂×D₄	1	2	yes	—
149	C₂²×C₄×C₅	C₂×D₄	1	2	yes	—
150	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
151	C₅×M₁₆	—	4	4	no	—
152	C₅×M₁₆	—	4	2	no	—
153	C₅×M₁₆	—	8	2	no	—
154	C₂×C₅×C₈	—	2	1	no	—
155	C₂×C₅×C₈	—	2	2	no	—
156	C₂×C₅×C₈	—	2	1	no	—
157	C₂×C₅×C₈	—	2	2	no	—
158	C₂×C₅×C₈	—	2	1	no	—
159	C₂×C₅×C₈	—	2	1	no	—
160	C₂×C₅×C₈	—	4	4	no	—
161	C₂×C₅×C₈	—	4	2	no	—
162	C₂×C₅×C₈	—	8	1	no	—
163	C₅×C₄⋊C₄	—	2	2	no	—
164	C₅×C₄⋊C₄	—	2	2	no	—
165	C₅×C₄⋊C₄	—	2	4	no	—
166	C₅×C₄⋊C₄	—	2	4	no	—
167	C₅×C₄⋊C₄	—	2	4	no	—
168	C₅×C₄⋊C₄	—	2	2	no	—
169	C₅×C₄⋊C₄	—	2	4	no	—
170	C₅×C₄⋊C₄	—	2	2	no	—
171	C₅×C₄⋊C₄	—	2	2	no	—
172	C₅×C₄⋊C₄	—	2	1	no	—
173	C₅×C₄⋊C₄	—	2	1	no	—
174	C₅×C₄⋊C₄	—	2	1	no	—
175	C₅×C₄⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
176	C₅×C₄⋊C₄	C₂²⋊C₄	1	2	yes	—
177	C₅×C₄⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
178	C₅×C₄⋊C₄	C₂²⋊C₄	1	2	yes	—
179	C₅×C₄⋊C₄	C₂²×C₄	1	4	yes	—
180	C₅×C₄⋊C₄	C₂²×C₄	1	2	yes	—
181	C₅×C₂²⋊C₄	—	2	2	no	—
182	C₅×C₂²⋊C₄	—	2	4	no	—
183	C₅×C₂²⋊C₄	—	2	4	no	—
184	C₅×C₂²⋊C₄	C₂²⋊C₄	1	2	yes	—
185	C₅×C₂²⋊C₄	C₂²⋊C₄	1	2	yes	—
186	C₅×C₂²⋊C₄	C₂²⋊C₄	1	2	yes	—
187	C₄²×C₅	—	2	4	no	—
188	C₄²×C₅	—	2	4	no	—
189	C₄²×C₅	—	2	2	no	—
190	C₄²×C₅	C₂²×C₄	1	2	yes	—
191	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
192	C₄²×C₅	C₂×D₄	1	2	yes	—
193	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
194	C₄²×C₅	C₂×D₄	1	2	yes	—
195	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
196	C₄²×C₅	C₂⁴	1	1	yes	characteristic
197	C₂×#131	—	2	1	no	—
198	#557	—	2	1	no	—
199	#557	C₄×C₅	1	2	yes	—
200	#556	—	2	1	no	—
201	#556	C₄×C₅	1	2	yes	—
202	#552	—	2	2	no	—
203	#552	C₄×C₅	1	4	yes	—
204	#541	—	2	2	no	—
205	#536	—	2	1	no	—
206	#533	C₂²×C₅	1	1	yes	characteristic
207	#533	C₂²×C₅	1	2	yes	—
208	#533	C₂²×C₅	1	2	yes	—
209	C₂×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
210	#519	—	2	1	no	—
211	C₄×#41	C₂²×C₅	1	1	yes	characteristic
212	#446	—	2	1	no	—
213	#436	—	2	1	no	—
214	#435	—	2	2	no	—
215	#432	C₂²×C₅	1	2	yes	—
216	#431	C₂²×C₅	1	1	yes	characteristic
217	#424	—	2	1	no	—
218	#424	—	2	2	no	—
219	#423	C₂²×C₅	1	1	yes	characteristic
220	#423	C₂²×C₅	1	2	yes	—
221	#423	C₂²×C₅	1	2	yes	—
222	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
223	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
224	C₂×C₄⋊C₈	C₂²×C₅	1	2	yes	—
225	#333	C₂²×C₅	1	1	yes	characteristic
226	#333	C₂²×C₅	1	1	yes	characteristic
227	#333	C₂²×C₅	1	2	yes	—
228	#332	C₂²×C₅	1	2	yes	—
229	#332	C₂²×C₅	1	2	yes	—
230	#332	C₂²×C₅	1	1	yes	characteristic
231	#332	C₂²×C₅	1	1	yes	characteristic
232	#332	C₂²×C₅	1	2	yes	—
233	#332	C₂²×C₅	1	2	yes	—
234	#332	C₂²×C₅	1	2	yes	—
235	C₂³×C₅	C₂×C₂²⋊C₄	1	2	yes	—
236	C₂³×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
237	C₅×Q₈	—	2	2	no	—
238	C₅×Q₈	—	4	2	no	—
239	C₅×Q₈	—	4	2	no	—
240	C₅×Q₈	—	4	2	no	—
241	C₅×Q₈	—	4	1	no	—
242	C₅×Q₈	—	4	1	no	—
243	C₅×Q₈	—	4	4	no	—
244	C₅×D₄	—	2	4	no	—
245	C₅×D₄	—	2	2	no	—
246	C₂×C₄×C₅	—	2	2	no	—
247	C₂×C₄×C₅	—	2	2	no	—
248	C₂×C₄×C₅	—	2	1	no	—
249	C₂×C₄×C₅	—	2	2	no	—
250	C₂×C₄×C₅	—	2	1	no	—
251	C₂×C₄×C₅	—	2	2	no	—
252	C₂×C₄×C₅	—	2	2	no	—
253	C₂×C₄×C₅	—	2	2	no	—
254	C₂×C₄×C₅	—	2	4	no	—
255	C₂×C₄×C₅	—	4	1	no	—
256	C₂×C₄×C₅	—	4	2	no	—
257	C₂×C₄×C₅	—	4	4	no	—
258	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	2	yes	—
259	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	2	yes	—
260	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
261	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	2	yes	—
262	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
263	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
264	C₂×C₄×C₅	AGL(1,ℤ/8)	1	2	yes	—
265	C₂×C₄×C₅	#137	1	2	yes	—
266	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
267	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
268	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
269	C₅×C₈	—	4	1	no	—
270	C₅×C₈	—	4	2	no	—
271	C₅×C₈	—	4	1	no	—
272	C₅×C₈	—	4	2	no	—
273	C₅×C₈	—	4	1	no	—
274	C₅×C₈	—	4	1	no	—
275	C₂×#41	C₅×D₄	1	1	yes	characteristic
276	C₂²×Q₈	—	2	1	no	—
277	#131	—	4	4	no	—
278	C₂×M₁₆	—	2	2	no	—
279	C₂×M₁₆	—	2	1	no	—
280	C₂×M₁₆	—	2	2	no	—
281	C₂²×C₈	—	2	2	no	—
282	C₂²×C₈	—	2	1	no	—
283	C₂²×C₈	—	2	1	no	—
284	C₄⋊Q₈	—	2	2	no	—
285	C₄⋊Q₈	—	2	1	no	—
286	C₄⋊Q₈	—	2	1	no	—
287	C₄⋊Q₈	C₂×C₄×C₅	1	2	yes	—
288	C₄⋊Q₈	C₂³×C₅	1	1	yes	characteristic
289	C₄⋊Q₈	C₂³×C₅	1	2	yes	—
290	C₄⋊Q₈	C₂³×C₅	1	1	yes	characteristic
291	#126	—	2	4	no	—
292	#126	—	2	4	no	—
293	#125	—	2	4	no	—
294	#125	—	2	4	no	—
295	#125	—	2	1	no	—
296	#125	—	2	2	no	—
297	#125	C₂×C₄×C₅	1	4	yes	—
298	#124	—	2	2	no	—
299	#123	—	2	4	no	—
300	C₂²⋊Q₈	—	2	2	no	—
301	C₂²⋊Q₈	—	2	2	no	—
302	C₂²⋊Q₈	—	2	1	no	—
303	C₂²⋊Q₈	—	2	2	no	—
304	C₂²⋊Q₈	C₂×C₄×C₅	1	2	yes	—
305	C₂²⋊Q₈	C₂×C₄×C₅	1	4	yes	—
306	C₄×Q₈	—	2	2	no	—
307	C₄×Q₈	—	2	2	no	—
308	C₄×Q₈	—	2	2	no	—
309	C₄×Q₈	—	2	2	no	—
310	C₄×Q₈	—	2	2	no	—
311	C₄×Q₈	—	2	1	no	—
312	C₄×Q₈	C₂×C₄×C₅	1	4	yes	—
313	C₄×Q₈	C₂×C₄×C₅	1	2	yes	—
314	C₄×Q₈	C₂×C₄×C₅	1	1	yes	characteristic
315	C₄×Q₈	C₅×D₄	1	1	yes	characteristic
316	C₄×D₄	C₂×C₄×C₅	1	2	yes	—
317	C₄×D₄	C₂×C₄×C₅	1	1	yes	characteristic
318	C₄×D₄	C₅×D₄	1	2	yes	—
319	C₄×D₄	C₅×D₄	1	1	yes	characteristic
320	#117	—	2	1	no	—
321	#117	—	2	2	no	—
322	#117	—	2	4	no	—
323	#117	C₂×C₄×C₅	1	4	yes	—
324	#117	C₅×D₄	1	1	yes	characteristic
325	#117	C₅×D₄	1	2	yes	—
326	C₂×C₄⋊C₄	—	2	1	no	—
327	C₂×C₄⋊C₄	C₂×C₄×C₅	1	2	yes	—
328	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
329	C₂×C₄²	C₂³×C₅	1	2	yes	—
330	C₄⋊C₈	—	2	2	no	—
331	C₄⋊C₈	—	2	1	no	—
332	C₄⋊C₈	—	2	1	no	—
333	C₄⋊C₈	—	2	2	no	—
334	C₄⋊C₈	—	2	1	no	—
335	C₄⋊C₈	—	2	2	no	—
336	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
337	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
338	C₄⋊C₈	C₂³×C₅	1	2	yes	—
339	C₄⋊C₈	C₂³×C₅	1	2	yes	—
340	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
341	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
342	C₂²⋊C₈	—	2	1	no	—
343	C₂²⋊C₈	—	2	2	no	—
344	#97	—	2	2	no	—
345	C₄×C₈	—	2	1	no	—
346	C₂²×C₅	—	2	1	no	—
347	C₂²×C₅	—	2	1	no	—
348	C₂²×C₅	—	2	2	no	—
349	C₂²×C₅	—	2	2	no	—
350	C₂²×C₅	—	2	2	no	—
351	C₂²×C₅	#417	1	2	yes	—
352	C₂²×C₅	C₂²×C₂²⋊C₄	1	1	yes	characteristic
353	C₄×C₅	—	2	1	no	—
354	C₄×C₅	—	2	2	no	—
355	C₄×C₅	—	2	1	no	—
356	C₄×C₅	—	2	2	no	—
357	C₄×C₅	—	2	1	no	—
358	C₄×C₅	—	2	2	no	—
359	C₄×C₅	—	4	2	no	—
360	C₄×C₅	—	4	4	no	—
361	C₄×C₅	—	4	2	no	—
362	C₄×C₅	#417	1	2	yes	—
363	C₄×C₅	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
364	C₄×C₅	C₂×#137	1	1	yes	characteristic
365	C₄×C₅	#577	1	1	yes	characteristic
366	C₄×C₅	#578	1	1	yes	characteristic
367	#41	—	2	2	no	—
368	#41	—	2	2	no	—
369	C₂×Q₈	—	2	2	no	—
370	C₂×Q₈	—	2	1	no	—
371	C₂×Q₈	—	2	2	no	—
372	C₂×Q₈	—	4	2	no	—
373	C₂×Q₈	—	4	2	no	—
374	C₂×Q₈	C₅×C₂²⋊C₄	1	1	yes	characteristic
375	C₂×Q₈	C₂²×C₄×C₅	1	2	yes	—
376	C₂×D₄	C₅×C₂²⋊C₄	1	2	yes	—
377	C₂×D₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
378	C₂²×C₄	—	2	2	no	—
379	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
380	C₂²×C₄	C₂²×C₄×C₅	1	2	yes	—
381	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
382	C₂²×C₄	C₂×C₅×D₄	1	2	yes	—
383	C₂²×C₄	C₂×C₅×D₄	1	2	yes	—
384	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
385	M₁₆	—	4	4	no	—
386	M₁₆	—	4	2	no	—
387	M₁₆	—	8	2	no	—
388	C₂×C₈	—	2	1	no	—
389	C₂×C₈	—	2	1	no	—
390	C₂×C₈	—	2	2	no	—
391	C₂×C₈	—	2	1	no	—
392	C₂×C₈	—	2	2	no	—
393	C₂×C₈	—	2	1	no	—
394	C₂×C₈	—	4	4	no	—
395	C₂×C₈	—	4	2	no	—
396	C₂×C₈	—	8	1	no	—
397	C₄⋊C₄	—	2	2	no	—
398	C₄⋊C₄	—	2	2	no	—
399	C₄⋊C₄	—	2	4	no	—
400	C₄⋊C₄	—	2	4	no	—
401	C₄⋊C₄	—	2	4	no	—
402	C₄⋊C₄	—	2	2	no	—
403	C₄⋊C₄	—	2	4	no	—
404	C₄⋊C₄	—	2	2	no	—
405	C₄⋊C₄	—	2	2	no	—
406	C₄⋊C₄	—	2	1	no	—
407	C₄⋊C₄	—	2	1	no	—
408	C₄⋊C₄	—	2	1	no	—
409	C₄⋊C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
410	C₄⋊C₄	C₅×C₂²⋊C₄	1	2	yes	—
411	C₄⋊C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
412	C₄⋊C₄	C₅×C₂²⋊C₄	1	2	yes	—
413	C₄⋊C₄	C₂²×C₄×C₅	1	4	yes	—
414	C₄⋊C₄	C₂²×C₄×C₅	1	2	yes	—
415	C₂²⋊C₄	—	2	2	no	—
416	C₂²⋊C₄	—	2	4	no	—
417	C₂²⋊C₄	—	2	4	no	—
418	C₂²⋊C₄	C₅×C₂²⋊C₄	1	2	yes	—
419	C₂²⋊C₄	C₅×C₂²⋊C₄	1	2	yes	—
420	C₂²⋊C₄	C₅×C₂²⋊C₄	1	2	yes	—
421	C₄²	—	2	4	no	—
422	C₄²	—	2	4	no	—
423	C₄²	—	2	2	no	—
424	C₄²	C₂²×C₄×C₅	1	2	yes	—
425	C₄²	C₂²×C₄×C₅	1	1	yes	characteristic
426	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
427	C₄²	C₂×C₅×D₄	1	2	yes	—
428	C₄²	C₂×C₅×D₄	1	2	yes	—
429	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
430	C₄²	C₂⁴×C₅	1	1	yes	characteristic
431	C₂×C₅	—	2	2	no	—
432	C₂×C₅	—	4	2	no	—
433	C₂×C₅	#2889	1	1	yes	characteristic
434	C₂×C₅	C₂×#417	1	1	yes	characteristic
435	C₂×C₅	#2898	1	1	yes	characteristic
436	C₂³	C₂×C₅×C₂²⋊C₄	1	2	yes	—
437	C₂³	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
438	Q₈	—	2	2	no	—
439	Q₈	—	4	2	no	—
440	Q₈	—	4	4	no	—
441	Q₈	—	4	2	no	—
442	Q₈	—	4	2	no	—
443	Q₈	—	4	1	no	—
444	Q₈	—	4	1	no	—
445	D₄	—	2	4	no	—
446	D₄	—	2	2	no	—
447	C₂×C₄	—	2	2	no	—
448	C₂×C₄	—	2	2	no	—
449	C₂×C₄	—	2	1	no	—
450	C₂×C₄	—	2	2	no	—
451	C₂×C₄	—	2	1	no	—
452	C₂×C₄	—	2	2	no	—
453	C₂×C₄	—	2	2	no	—
454	C₂×C₄	—	2	2	no	—
455	C₂×C₄	—	2	4	no	—
456	C₂×C₄	—	4	1	no	—
457	C₂×C₄	—	4	2	no	—
458	C₂×C₄	—	4	4	no	—
459	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	2	yes	—
460	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	2	yes	—
461	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
462	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	2	yes	—
463	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
464	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
465	C₂×C₄	C₅×AGL(1,ℤ/8)	1	2	yes	—
466	C₂×C₄	C₅×#137	1	2	yes	—
467	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
468	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
469	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
470	C₈	—	4	1	no	—
471	C₈	—	4	2	no	—
472	C₈	—	4	1	no	—
473	C₈	—	4	2	no	—
474	C₈	—	4	1	no	—
475	C₈	—	4	1	no	—
476	C₅	#17763	1	1	yes	characteristic, direct product factor, Sylow
477	C₂²	—	2	1	no	—
478	C₂²	—	2	1	no	—
479	C₂²	—	2	2	no	—
480	C₂²	—	2	2	no	—
481	C₂²	—	2	2	no	—
482	C₂²	C₅×#417	1	2	yes	—
483	C₂²	C₂²×C₅×C₂²⋊C₄	1	1	yes	characteristic
484	C₄	—	2	1	no	—
485	C₄	—	2	2	no	—
486	C₄	—	2	1	no	—
487	C₄	—	2	2	no	—
488	C₄	—	2	1	no	—
489	C₄	—	2	2	no	—
490	C₄	—	4	2	no	—
491	C₄	—	4	4	no	—
492	C₄	—	4	2	no	—
493	C₄	C₅×#417	1	2	yes	—
494	C₄	C₂×C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
495	C₄	C₂×C₅×#137	1	1	yes	characteristic
496	C₄	C₅×#577	1	1	yes	characteristic
497	C₄	C₅×#578	1	1	yes	characteristic
498	C₂	—	2	2	no	—
499	C₂	—	4	2	no	—
500	C₂	C₅×#2889	1	1	yes	characteristic
501	C₂	C₂×C₅×#417	1	1	yes	characteristic
502	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	C₂×C₅×#41	D₄
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
4. C₅×#1561	C₂	semidirect
5. C₅×#1559	C₂	semidirect
6. C₅×#1552	C₂	semidirect
7. C₅×#1550	C₂	semidirect
8. C₅×#1550	C₂	semidirect
9. C₅×#1546	C₂	semidirect
10. C₅×#1542	C₂	semidirect
11. C₂×C₅×#332	C₂	semidirect
50. #17763	C₅	direct (N × H)
125. #1561	C₂×C₅	semidirect
126. #1559	C₂×C₅	semidirect
127. #1552	C₂×C₅	semidirect
128. #1550	C₂×C₅	semidirect
129. #1550	C₂×C₅	semidirect
130. #1546	C₂×C₅	semidirect
131. #1542	C₂×C₅	semidirect
132. C₂×#332	C₂×C₅	semidirect
476. C₅	#17763	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×#3509	2
C₅×#2989	2
C₅×#2906	2
C₅×#1561	2
C₅×#1559	2
C₅×#1552	2
C₅×#1550	2
C₅×#1546	2
C₅×#1542	2
C₂×C₅×#332	2
#17763	5

Subgroups — C5×#17763 #11940483

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#17763 #11940483