Subgroups — C₅×#17749 #11940469

Order 1280.

996 conjugacy classes of subgroups.

The subgroup lattice has 532 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#533	C₂	1	1	yes	maximal, characteristic
2	C₅×#2920	C₂	1	1	yes	maximal, characteristic
3	C₂×C₅×#423	C₂	1	1	yes	maximal, characteristic
4	C₅×#1559	C₂	1	4	yes	maximal, complemented
5	C₅×#1550	C₂	1	4	yes	maximal, complemented
6	C₅×#1548	C₂	1	2	yes	maximal, complemented
7	C₅×#1546	C₂	1	2	yes	maximal, complemented
8	C₂²×C₅×M₁₆	—	2	1	no	—
9	C₅×#533	—	2	1	no	—
10	C₅×#533	—	2	1	no	—
11	C₅×#533	—	2	1	no	—
12	C₅×#533	—	2	1	no	—
13	C₅×#533	C₄	1	2	yes	—
14	C₅×#533	C₄	1	2	yes	—
15	C₅×#533	C₂²	1	2	yes	—
16	C₅×#533	C₂²	1	2	yes	—
17	C₂×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
18	C₂×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
19	C₂×C₅×#125	—	2	1	no	—
20	C₂×C₅×C₂²⋊Q₈	—	2	1	no	—
21	C₂×C₅×C₂²⋊Q₈	C₄	1	2	yes	—
22	C₂×C₄×C₅×Q₈	—	2	1	no	—
23	C₂×C₄×C₅×Q₈	C₄	1	2	yes	—
24	C₂×C₅×#117	—	2	1	no	—
25	C₂²×C₄²×C₅	C₂²	1	1	yes	characteristic
26	C₅×#432	—	2	1	no	—
27	C₅×#432	C₂²	1	2	yes	—
28	C₅×#431	—	2	1	no	—
29	C₅×#431	C₂²	1	2	yes	—
30	C₅×#423	—	2	1	no	—
31	C₅×#423	—	2	1	no	—
32	C₅×#423	C₂²	1	2	yes	—
33	C₅×#423	C₂²	1	2	yes	—
34	C₅×#423	C₂²	1	2	yes	—
35	C₂×C₅×C₄⋊C₈	—	2	1	no	—
36	C₂×C₅×C₄⋊C₈	C₂²	1	2	yes	—
37	C₅×#407	—	2	1	no	—
38	C₄×C₅×M₁₆	—	2	1	no	—
39	C₅×#333	C₂²	1	8	yes	complemented
40	C₅×#332	C₂²	1	8	yes	complemented
41	#17749	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
42	C₂²×C₅×Q₈	—	2	1	no	—
43	C₂²×C₅×Q₈	C₂×C₄	1	2	yes	—
44	C₂³×C₄×C₅	C₂×C₄	1	1	yes	characteristic
45	C₂³×C₄×C₅	D₄	1	1	yes	characteristic
46	C₂³×C₄×C₅	D₄	1	1	yes	characteristic
47	C₂×C₅×M₁₆	—	2	2	no	—
48	C₂×C₅×M₁₆	—	2	2	no	—
49	C₂×C₅×M₁₆	—	2	2	no	—
50	C₂×C₅×M₁₆	—	4	4	no	—
51	C₂²×C₅×C₈	—	2	2	no	—
52	C₅×C₄⋊Q₈	—	2	1	no	—
53	C₅×C₄⋊Q₈	—	2	1	no	—
54	C₅×C₄⋊Q₈	—	2	1	no	—
55	C₅×C₄⋊Q₈	—	2	1	no	—
56	C₅×C₄⋊Q₈	C₂×C₄	1	2	yes	—
57	C₅×C₄⋊Q₈	C₂×C₄	1	2	yes	—
58	C₅×C₄⋊Q₈	C₂³	1	2	yes	—
59	C₅×C₄⋊Q₈	C₂³	1	2	yes	—
60	C₅×#125	—	2	2	no	—
61	C₅×#125	—	2	2	no	—
62	C₅×#125	—	2	2	no	—
63	C₅×#125	—	2	2	no	—
64	C₅×C₂²⋊Q₈	—	2	2	no	—
65	C₅×C₂²⋊Q₈	—	2	2	no	—
66	C₅×C₂²⋊Q₈	—	2	2	no	—
67	C₅×C₂²⋊Q₈	—	2	2	no	—
68	C₅×C₂²⋊Q₈	—	2	2	no	—
69	C₅×C₂²⋊Q₈	—	2	2	no	—
70	C₅×C₂²⋊Q₈	C₂×C₄	1	4	yes	—
71	C₅×C₂²⋊Q₈	C₂×C₄	1	4	yes	—
72	C₄×C₅×Q₈	—	2	2	no	—
73	C₄×C₅×Q₈	—	2	2	no	—
74	C₄×C₅×Q₈	—	2	2	no	—
75	C₄×C₅×Q₈	—	2	2	no	—
76	C₄×C₅×Q₈	—	2	2	no	—
77	C₄×C₅×Q₈	—	2	2	no	—
78	C₄×C₅×Q₈	C₂×C₄	1	4	yes	—
79	C₄×C₅×Q₈	C₂×C₄	1	4	yes	—
80	C₅×#117	—	2	2	no	—
81	C₅×#117	—	2	2	no	—
82	C₅×#117	—	2	2	no	—
83	C₅×#117	—	2	2	no	—
84	C₂×C₅×C₄⋊C₄	—	2	2	no	—
85	C₂×C₅×C₄⋊C₄	—	2	2	no	—
86	C₂×C₅×C₄⋊C₄	—	2	1	no	—
87	C₂×C₅×C₄⋊C₄	—	2	1	no	—
88	C₂×C₅×C₄⋊C₄	—	2	1	no	—
89	C₂×C₅×C₄⋊C₄	C₂×C₄	1	2	yes	—
90	C₂×C₅×C₂²⋊C₄	—	2	2	no	—
91	C₂×C₄²×C₅	—	2	2	no	—
92	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
93	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
94	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
95	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
96	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
97	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
98	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
99	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
100	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
101	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
102	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
103	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
104	C₅×C₄⋊C₈	—	2	2	no	—
105	C₅×C₄⋊C₈	—	2	2	no	—
106	C₅×C₄⋊C₈	—	2	2	no	—
107	C₅×C₄⋊C₈	—	2	2	no	—
108	C₅×C₄⋊C₈	C₂³	1	4	yes	—
109	C₅×C₄⋊C₈	C₂³	1	4	yes	—
110	C₅×C₂²⋊C₈	—	2	2	no	—
111	C₅×C₂²⋊C₈	—	2	2	no	—
112	C₅×#97	—	2	2	no	—
113	C₄×C₅×C₈	—	2	2	no	—
114	C₂×#533	C₂×C₅	1	1	yes	characteristic
115	#2920	C₂×C₅	1	1	yes	characteristic
116	C₂×#423	C₂×C₅	1	1	yes	characteristic
117	#1559	C₂×C₅	1	4	yes	complemented
118	#1550	C₂×C₅	1	4	yes	complemented
119	#1548	C₂×C₅	1	2	yes	complemented
120	#1546	C₂×C₅	1	2	yes	complemented
121	C₂⁴×C₅	C₂²⋊C₄	1	1	yes	characteristic
122	C₂×C₅×Q₈	—	2	2	no	—
123	C₂×C₅×Q₈	—	2	2	no	—
124	C₂×C₅×Q₈	—	2	2	no	—
125	C₂×C₅×Q₈	—	4	4	no	—
126	C₂×C₅×Q₈	—	4	2	no	—
127	C₂×C₅×Q₈	—	4	2	no	—
128	C₂×C₅×Q₈	C₂²×C₄	1	4	yes	—
129	C₂²×C₄×C₅	—	2	2	no	—
130	C₂²×C₄×C₅	—	2	2	no	—
131	C₂²×C₄×C₅	—	2	4	no	—
132	C₂²×C₄×C₅	—	2	2	no	—
133	C₂²×C₄×C₅	—	2	2	no	—
134	C₂²×C₄×C₅	—	4	2	no	—
135	C₂²×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
136	C₂²×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
137	C₂²×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
138	C₂²×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
139	C₂²×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
140	C₂²×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
141	C₂²×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
142	C₂²×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
143	C₂²×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
144	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
145	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
146	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
147	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
148	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
149	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
150	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
151	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
152	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
153	C₅×M₁₆	—	4	4	no	—
154	C₅×M₁₆	—	4	4	no	—
155	C₅×M₁₆	—	4	4	no	—
156	C₂×C₅×C₈	—	2	4	no	—
157	C₂×C₅×C₈	—	2	4	no	—
158	C₂×C₅×C₈	—	4	4	no	—
159	C₅×C₄⋊C₄	—	2	2	no	—
160	C₅×C₄⋊C₄	—	2	2	no	—
161	C₅×C₄⋊C₄	—	2	2	no	—
162	C₅×C₄⋊C₄	—	2	4	no	—
163	C₅×C₄⋊C₄	—	2	4	no	—
164	C₅×C₄⋊C₄	—	2	4	no	—
165	C₅×C₄⋊C₄	—	2	4	no	—
166	C₅×C₄⋊C₄	—	2	2	no	—
167	C₅×C₄⋊C₄	—	2	2	no	—
168	C₅×C₄⋊C₄	—	2	2	no	—
169	C₅×C₄⋊C₄	—	2	2	no	—
170	C₅×C₄⋊C₄	C₂²×C₄	1	4	yes	—
171	C₅×C₂²⋊C₄	—	2	4	no	—
172	C₅×C₂²⋊C₄	—	2	4	no	—
173	C₄²×C₅	—	2	4	no	—
174	C₄²×C₅	—	2	4	no	—
175	C₄²×C₅	C₂²⋊C₄	1	1	yes	characteristic
176	C₄²×C₅	C₂²⋊C₄	1	1	yes	characteristic
177	C₄²×C₅	C₂²⋊C₄	1	1	yes	characteristic
178	C₄²×C₅	C₂²⋊C₄	1	1	yes	characteristic
179	C₄²×C₅	C₂²⋊C₄	1	1	yes	characteristic
180	C₄²×C₅	C₂²⋊C₄	1	1	yes	characteristic
181	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
182	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
183	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
184	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
185	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
186	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
187	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
188	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
189	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
190	C₄²×C₅	C₂⁴	1	1	yes	characteristic
191	C₂²×M₁₆	—	2	1	no	—
192	#533	—	2	1	no	—
193	#533	—	2	1	no	—
194	#533	—	2	1	no	—
195	#533	—	2	1	no	—
196	#533	C₄×C₅	1	2	yes	—
197	#533	C₄×C₅	1	2	yes	—
198	#533	C₂²×C₅	1	2	yes	—
199	#533	C₂²×C₅	1	2	yes	—
200	C₂×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
201	C₂×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
202	C₂×#125	—	2	1	no	—
203	C₂×C₂²⋊Q₈	—	2	1	no	—
204	C₂×C₂²⋊Q₈	C₄×C₅	1	2	yes	—
205	C₂×C₄×Q₈	—	2	1	no	—
206	C₂×C₄×Q₈	C₄×C₅	1	2	yes	—
207	C₂×#117	—	2	1	no	—
208	C₂²×C₄²	C₂²×C₅	1	1	yes	characteristic
209	#432	—	2	1	no	—
210	#432	C₂²×C₅	1	2	yes	—
211	#431	—	2	1	no	—
212	#431	C₂²×C₅	1	2	yes	—
213	#423	—	2	1	no	—
214	#423	—	2	1	no	—
215	#423	C₂²×C₅	1	2	yes	—
216	#423	C₂²×C₅	1	2	yes	—
217	#423	C₂²×C₅	1	2	yes	—
218	C₂×C₄⋊C₈	—	2	1	no	—
219	C₂×C₄⋊C₈	C₂²×C₅	1	2	yes	—
220	#407	—	2	1	no	—
221	C₄×M₁₆	—	2	1	no	—
222	#333	C₂²×C₅	1	8	yes	complemented
223	#332	C₂²×C₅	1	8	yes	complemented
224	C₂³×C₅	—	2	2	no	—
225	C₂³×C₅	—	2	2	no	—
226	C₂³×C₅	—	4	1	no	—
227	C₂³×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
228	C₂³×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
229	C₂³×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
230	C₅×Q₈	—	4	4	no	—
231	C₅×Q₈	—	4	2	no	—
232	C₅×Q₈	—	4	2	no	—
233	C₅×Q₈	—	4	4	no	—
234	C₅×Q₈	—	4	4	no	—
235	C₂×C₄×C₅	—	2	2	no	—
236	C₂×C₄×C₅	—	2	2	no	—
237	C₂×C₄×C₅	—	2	1	no	—
238	C₂×C₄×C₅	—	2	1	no	—
239	C₂×C₄×C₅	—	2	2	no	—
240	C₂×C₄×C₅	—	2	2	no	—
241	C₂×C₄×C₅	—	2	1	no	—
242	C₂×C₄×C₅	—	2	1	no	—
243	C₂×C₄×C₅	—	2	2	no	—
244	C₂×C₄×C₅	—	2	2	no	—
245	C₂×C₄×C₅	—	2	2	no	—
246	C₂×C₄×C₅	—	2	2	no	—
247	C₂×C₄×C₅	—	2	2	no	—
248	C₂×C₄×C₅	—	2	2	no	—
249	C₂×C₄×C₅	—	2	2	no	—
250	C₂×C₄×C₅	—	2	4	no	—
251	C₂×C₄×C₅	—	2	4	no	—
252	C₂×C₄×C₅	—	4	1	no	—
253	C₂×C₄×C₅	—	4	1	no	—
254	C₂×C₄×C₅	—	4	1	no	—
255	C₂×C₄×C₅	—	4	4	no	—
256	C₂×C₄×C₅	—	4	4	no	—
257	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
258	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
259	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
260	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
261	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
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	C₂×C₂²⋊C₄	1	1	yes	characteristic
265	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
266	C₂×C₄×C₅	AGL(1,ℤ/8)	1	2	yes	—
267	C₂×C₄×C₅	#137	1	2	yes	—
268	C₂×C₄×C₅	#137	1	4	yes	—
269	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
270	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
271	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
272	C₅×C₈	—	4	4	no	—
273	C₅×C₈	—	4	4	no	—
274	C₂²×Q₈	—	2	1	no	—
275	C₂²×Q₈	C₂×C₄×C₅	1	2	yes	—
276	C₂³×C₄	C₂×C₄×C₅	1	1	yes	characteristic
277	C₂³×C₄	C₅×D₄	1	1	yes	characteristic
278	C₂³×C₄	C₅×D₄	1	1	yes	characteristic
279	C₂×M₁₆	—	2	2	no	—
280	C₂×M₁₆	—	2	2	no	—
281	C₂×M₁₆	—	2	2	no	—
282	C₂×M₁₆	—	4	4	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	—	2	1	no	—
288	C₄⋊Q₈	C₂×C₄×C₅	1	2	yes	—
289	C₄⋊Q₈	C₂×C₄×C₅	1	2	yes	—
290	C₄⋊Q₈	C₂³×C₅	1	2	yes	—
291	C₄⋊Q₈	C₂³×C₅	1	2	yes	—
292	#125	—	2	2	no	—
293	#125	—	2	2	no	—
294	#125	—	2	2	no	—
295	#125	—	2	2	no	—
296	C₂²⋊Q₈	—	2	2	no	—
297	C₂²⋊Q₈	—	2	2	no	—
298	C₂²⋊Q₈	—	2	2	no	—
299	C₂²⋊Q₈	—	2	2	no	—
300	C₂²⋊Q₈	—	2	2	no	—
301	C₂²⋊Q₈	—	2	2	no	—
302	C₂²⋊Q₈	C₂×C₄×C₅	1	4	yes	—
303	C₂²⋊Q₈	C₂×C₄×C₅	1	4	yes	—
304	C₄×Q₈	—	2	2	no	—
305	C₄×Q₈	—	2	2	no	—
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	C₂×C₄×C₅	1	4	yes	—
311	C₄×Q₈	C₂×C₄×C₅	1	4	yes	—
312	#117	—	2	2	no	—
313	#117	—	2	2	no	—
314	#117	—	2	2	no	—
315	#117	—	2	2	no	—
316	C₂×C₄⋊C₄	—	2	2	no	—
317	C₂×C₄⋊C₄	—	2	2	no	—
318	C₂×C₄⋊C₄	—	2	1	no	—
319	C₂×C₄⋊C₄	—	2	1	no	—
320	C₂×C₄⋊C₄	—	2	1	no	—
321	C₂×C₄⋊C₄	C₂×C₄×C₅	1	2	yes	—
322	C₂×C₂²⋊C₄	—	2	2	no	—
323	C₂×C₄²	—	2	2	no	—
324	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
325	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
326	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
327	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
328	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
329	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
330	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
331	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
332	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
333	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
334	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
335	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
336	C₄⋊C₈	—	2	2	no	—
337	C₄⋊C₈	—	2	2	no	—
338	C₄⋊C₈	—	2	2	no	—
339	C₄⋊C₈	—	2	2	no	—
340	C₄⋊C₈	C₂³×C₅	1	4	yes	—
341	C₄⋊C₈	C₂³×C₅	1	4	yes	—
342	C₂²⋊C₈	—	2	2	no	—
343	C₂²⋊C₈	—	2	2	no	—
344	#97	—	2	2	no	—
345	C₄×C₈	—	2	2	no	—
346	C₂²×C₅	—	2	1	no	—
347	C₂²×C₅	—	2	1	no	—
348	C₂²×C₅	—	2	1	no	—
349	C₂²×C₅	—	2	1	no	—
350	C₂²×C₅	—	2	1	no	—
351	C₂²×C₅	—	2	1	no	—
352	C₂²×C₅	—	2	1	no	—
353	C₂²×C₅	—	4	4	no	—
354	C₂²×C₅	#417	1	2	yes	—
355	C₂²×C₅	#419	1	2	yes	—
356	C₂²×C₅	C₂²×C₂²⋊C₄	1	1	yes	characteristic
357	C₄×C₅	—	2	1	no	—
358	C₄×C₅	—	2	1	no	—
359	C₄×C₅	—	2	1	no	—
360	C₄×C₅	—	2	1	no	—
361	C₄×C₅	—	2	1	no	—
362	C₄×C₅	—	2	1	no	—
363	C₄×C₅	—	2	1	no	—
364	C₄×C₅	—	4	4	no	—
365	C₄×C₅	—	4	4	no	—
366	C₄×C₅	#413	1	2	yes	—
367	C₄×C₅	#417	1	2	yes	—
368	C₄×C₅	#419	1	2	yes	—
369	C₄×C₅	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
370	C₄×C₅	C₂×#137	1	2	yes	—
371	C₄×C₅	C₂×#137	1	1	yes	characteristic
372	C₂⁴	C₅×C₂²⋊C₄	1	1	yes	characteristic
373	C₂×Q₈	—	2	2	no	—
374	C₂×Q₈	—	2	2	no	—
375	C₂×Q₈	—	2	2	no	—
376	C₂×Q₈	—	4	4	no	—
377	C₂×Q₈	—	4	2	no	—
378	C₂×Q₈	—	4	2	no	—
379	C₂×Q₈	C₂²×C₄×C₅	1	4	yes	—
380	C₂²×C₄	—	2	2	no	—
381	C₂²×C₄	—	2	2	no	—
382	C₂²×C₄	—	2	4	no	—
383	C₂²×C₄	—	2	2	no	—
384	C₂²×C₄	—	2	2	no	—
385	C₂²×C₄	—	4	2	no	—
386	C₂²×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
387	C₂²×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
388	C₂²×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
389	C₂²×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
390	C₂²×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
391	C₂²×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
392	C₂²×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
393	C₂²×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
394	C₂²×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
395	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
396	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
397	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
398	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
399	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
400	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
401	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
402	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
403	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
404	M₁₆	—	4	4	no	—
405	M₁₆	—	4	4	no	—
406	M₁₆	—	4	4	no	—
407	C₂×C₈	—	2	4	no	—
408	C₂×C₈	—	2	4	no	—
409	C₂×C₈	—	4	4	no	—
410	C₄⋊C₄	—	2	2	no	—
411	C₄⋊C₄	—	2	2	no	—
412	C₄⋊C₄	—	2	2	no	—
413	C₄⋊C₄	—	2	4	no	—
414	C₄⋊C₄	—	2	4	no	—
415	C₄⋊C₄	—	2	4	no	—
416	C₄⋊C₄	—	2	4	no	—
417	C₄⋊C₄	—	2	2	no	—
418	C₄⋊C₄	—	2	2	no	—
419	C₄⋊C₄	—	2	2	no	—
420	C₄⋊C₄	—	2	2	no	—
421	C₄⋊C₄	C₂²×C₄×C₅	1	4	yes	—
422	C₂²⋊C₄	—	2	4	no	—
423	C₂²⋊C₄	—	2	4	no	—
424	C₄²	—	2	4	no	—
425	C₄²	—	2	4	no	—
426	C₄²	C₅×C₂²⋊C₄	1	1	yes	characteristic
427	C₄²	C₅×C₂²⋊C₄	1	1	yes	characteristic
428	C₄²	C₅×C₂²⋊C₄	1	1	yes	characteristic
429	C₄²	C₅×C₂²⋊C₄	1	1	yes	characteristic
430	C₄²	C₅×C₂²⋊C₄	1	1	yes	characteristic
431	C₄²	C₅×C₂²⋊C₄	1	1	yes	characteristic
432	C₄²	C₂²×C₄×C₅	1	1	yes	characteristic
433	C₄²	C₂²×C₄×C₅	1	1	yes	characteristic
434	C₄²	C₂²×C₄×C₅	1	1	yes	characteristic
435	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
436	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
437	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
438	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
439	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
440	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
441	C₄²	C₂⁴×C₅	1	1	yes	characteristic
442	C₂×C₅	—	2	2	no	—
443	C₂×C₅	—	2	2	no	—
444	C₂×C₅	—	4	1	no	—
445	C₂×C₅	C₂×#413	1	1	yes	characteristic
446	C₂×C₅	C₂×#419	1	1	yes	characteristic
447	C₂×C₅	C₂×#417	1	1	yes	characteristic
448	C₂³	—	2	2	no	—
449	C₂³	—	2	2	no	—
450	C₂³	—	4	1	no	—
451	C₂³	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
452	C₂³	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
453	C₂³	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
454	Q₈	—	4	4	no	—
455	Q₈	—	4	4	no	—
456	Q₈	—	4	4	no	—
457	Q₈	—	4	2	no	—
458	Q₈	—	4	2	no	—
459	C₂×C₄	—	2	2	no	—
460	C₂×C₄	—	2	2	no	—
461	C₂×C₄	—	2	2	no	—
462	C₂×C₄	—	2	2	no	—
463	C₂×C₄	—	2	2	no	—
464	C₂×C₄	—	2	2	no	—
465	C₂×C₄	—	2	2	no	—
466	C₂×C₄	—	2	2	no	—
467	C₂×C₄	—	2	2	no	—
468	C₂×C₄	—	2	1	no	—
469	C₂×C₄	—	2	1	no	—
470	C₂×C₄	—	2	2	no	—
471	C₂×C₄	—	2	2	no	—
472	C₂×C₄	—	2	1	no	—
473	C₂×C₄	—	2	1	no	—
474	C₂×C₄	—	2	4	no	—
475	C₂×C₄	—	2	4	no	—
476	C₂×C₄	—	4	1	no	—
477	C₂×C₄	—	4	1	no	—
478	C₂×C₄	—	4	1	no	—
479	C₂×C₄	—	4	4	no	—
480	C₂×C₄	—	4	4	no	—
481	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
482	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
483	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
484	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
485	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
486	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
487	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
488	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
489	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
490	C₂×C₄	C₅×AGL(1,ℤ/8)	1	2	yes	—
491	C₂×C₄	C₅×#137	1	2	yes	—
492	C₂×C₄	C₅×#137	1	4	yes	—
493	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
494	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
495	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
496	C₈	—	4	4	no	—
497	C₈	—	4	4	no	—
498	C₅	#17749	1	1	yes	characteristic, direct product factor, Sylow
499	C₂²	—	2	1	no	—
500	C₂²	—	2	1	no	—
501	C₂²	—	2	1	no	—
502	C₂²	—	2	1	no	—
503	C₂²	—	2	1	no	—
504	C₂²	—	2	1	no	—
505	C₂²	—	2	1	no	—
506	C₂²	—	4	4	no	—
507	C₂²	C₅×#417	1	2	yes	—
508	C₂²	C₅×#419	1	2	yes	—
509	C₂²	C₂²×C₅×C₂²⋊C₄	1	1	yes	characteristic
510	C₄	—	2	1	no	—
511	C₄	—	2	1	no	—
512	C₄	—	2	1	no	—
513	C₄	—	2	1	no	—
514	C₄	—	2	1	no	—
515	C₄	—	2	1	no	—
516	C₄	—	2	1	no	—
517	C₄	—	4	4	no	—
518	C₄	—	4	4	no	—
519	C₄	C₅×#413	1	2	yes	—
520	C₄	C₅×#417	1	2	yes	—
521	C₄	C₅×#419	1	2	yes	—
522	C₄	C₂×C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
523	C₄	C₂×C₅×#137	1	2	yes	—
524	C₄	C₂×C₅×#137	1	1	yes	characteristic
525	C₂	—	2	2	no	—
526	C₂	—	2	2	no	—
527	C₂	—	4	1	no	—
528	C₂	C₂×C₅×#413	1	1	yes	characteristic
529	C₂	C₂×C₅×#419	1	1	yes	characteristic
530	C₂	C₂×C₅×#417	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	C₂⁴×C₅	C₂²⋊C₄
LCS	G ▷ C₂×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₅ ◁ C₂²×C₄²×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
4. C₅×#1559	C₂	semidirect
5. C₅×#1550	C₂	semidirect
6. C₅×#1548	C₂	semidirect
7. C₅×#1546	C₂	semidirect
39. C₅×#333	C₂²	semidirect
40. C₅×#332	C₂²	semidirect
41. #17749	C₅	direct (N × H)
117. #1559	C₂×C₅	semidirect
118. #1550	C₂×C₅	semidirect
119. #1548	C₂×C₅	semidirect
120. #1546	C₂×C₅	semidirect
222. #333	C₂²×C₅	semidirect
223. #332	C₂²×C₅	semidirect
498. C₅	#17749	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₅×#533	2
C₅×#2920	2
C₂×C₅×#423	2
C₅×#1559	2
C₅×#1550	2
C₅×#1548	2
C₅×#1546	2
#17749	5

Subgroups — C5×#17749 #11940469

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#17749 #11940469