Subgroups — C₂×C₅×#3182 #11983409

Order 1280.

2234 conjugacy classes of subgroups.

The subgroup lattice has 498 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, complemented
2	C₂×C₅×#532	C₂	1	1	yes	maximal, characteristic
3	C₅×#3182	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₅×#500	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₅×#492	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₅×#487	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₅×#486	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₅×#468	C₂	1	4	yes	maximal, complemented
9	C₂×C₅×#440	C₂	1	4	yes	maximal, complemented
10	C₂×C₄×C₅×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂²×C₅×#41	—	2	1	no	—
12	C₂²×C₅×SD₁₆	C₂²	1	4	yes	—
13	C₂²×C₅×M₁₆	C₂²	1	2	yes	—
14	C₅×#533	—	2	4	no	—
15	C₅×#533	C₂²	1	8	yes	complemented
16	C₅×#532	—	2	4	no	—
17	C₅×#532	C₂²	1	8	yes	—
18	C₂×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
19	C₂×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
20	C₂×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
21	C₂×C₅×#127	C₂²	1	1	yes	characteristic
22	C₂×C₅×#125	—	2	1	no	—
23	C₂×C₅×#124	—	2	1	no	—
24	C₂×C₅×C₂²⋊Q₈	—	2	1	no	—
25	C₂×C₅×C₂²⋊Q₈	C₂²	1	2	yes	—
26	C₂×C₅×#121	—	2	1	no	—
27	C₂×C₅×#121	C₂²	1	2	yes	—
28	C₂×C₄×C₅×Q₈	—	2	1	no	—
29	C₂×C₄×C₅×Q₈	C₂²	1	2	yes	—
30	C₂×C₄×C₅×D₄	—	2	1	no	—
31	C₂×C₄×C₅×D₄	C₂²	1	2	yes	—
32	C₂×C₅×#117	—	2	1	no	—
33	C₂²×C₄²×C₅	C₂²	1	1	yes	characteristic
34	C₅×#500	C₂²	1	8	yes	complemented
35	C₅×#492	C₂²	1	8	yes	complemented
36	C₅×#487	C₂²	1	8	yes	complemented
37	C₅×#486	C₂²	1	8	yes	complemented
38	C₅×#468	C₂²	1	32	yes	complemented
39	C₅×#440	C₂²	1	32	yes	complemented
40	C₂×C₅×#107	C₂²	1	4	yes	—
41	C₂×C₅×#103	C₂²	1	4	yes	—
42	C₂×C₅×#102	C₂²	1	4	yes	—
43	C₄×C₅×M₁₆	C₂²	1	8	yes	complemented
44	C₂×C₅×#97	C₂²	1	2	yes	—
45	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
46	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
47	C₂×#3182	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
48	C₂×C₅×#41	—	2	8	no	—
49	C₂×C₅×#41	—	4	8	no	—
50	C₂²×C₅×Q₈	—	2	1	no	—
51	C₂²×C₅×Q₈	—	2	1	no	—
52	C₂²×C₅×Q₈	C₂³	1	2	yes	—
53	C₂²×C₅×D₄	—	2	2	no	—
54	C₂²×C₅×D₄	—	2	1	no	—
55	C₂²×C₅×D₄	—	2	1	no	—
56	C₂²×C₅×D₄	C₂³	1	2	yes	—
57	C₂³×C₄×C₅	—	2	2	no	—
58	C₂³×C₄×C₅	D₄	1	1	yes	characteristic
59	C₂³×C₄×C₅	D₄	1	1	yes	characteristic
60	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
61	C₂×C₅×SD₁₆	—	2	16	no	—
62	C₂×C₅×SD₁₆	C₂³	1	16	yes	—
63	C₂×C₅×M₁₆	—	2	8	no	—
64	C₂×C₅×M₁₆	C₂³	1	8	yes	—
65	C₂²×C₅×C₈	C₂³	1	2	yes	—
66	C₂²×C₅×C₈	C₂³	1	2	yes	—
67	C₅×C₄⋊Q₈	—	2	2	no	—
68	C₅×C₄⋊Q₈	—	2	2	no	—
69	C₅×C₄⋊Q₈	—	2	2	no	—
70	C₅×C₄⋊Q₈	C₂³	1	4	yes	—
71	C₅×C₄⋊Q₈	C₂³	1	4	yes	—
72	C₅×C₄⋊Q₈	C₂³	1	4	yes	—
73	C₅×#127	—	2	2	no	—
74	C₅×#127	C₂³	1	4	yes	—
75	C₅×#125	—	2	8	no	—
76	C₅×#124	—	2	8	no	—
77	C₅×C₂²⋊Q₈	—	2	8	no	—
78	C₅×C₂²⋊Q₈	—	2	4	no	—
79	C₅×C₂²⋊Q₈	C₂³	1	8	yes	—
80	C₅×#121	—	2	8	no	—
81	C₅×#121	—	2	4	no	—
82	C₅×#121	C₂³	1	8	yes	—
83	C₄×C₅×Q₈	—	2	8	no	—
84	C₄×C₅×Q₈	—	2	4	no	—
85	C₄×C₅×Q₈	C₂³	1	8	yes	—
86	C₄×C₅×D₄	—	2	8	no	—
87	C₄×C₅×D₄	—	2	4	no	—
88	C₄×C₅×D₄	C₂³	1	8	yes	—
89	C₅×#117	—	2	8	no	—
90	C₂×C₅×C₄⋊C₄	—	2	1	no	—
91	C₂×C₅×C₄⋊C₄	—	2	1	no	—
92	C₂×C₅×C₄⋊C₄	—	2	1	no	—
93	C₂×C₅×C₄⋊C₄	—	2	1	no	—
94	C₂×C₅×C₄⋊C₄	—	2	2	no	—
95	C₂×C₅×C₄⋊C₄	—	2	2	no	—
96	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
97	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
98	C₂×C₅×C₂²⋊C₄	—	2	2	no	—
99	C₂×C₅×C₂²⋊C₄	—	2	2	no	—
100	C₂×C₅×C₂²⋊C₄	—	2	2	no	—
101	C₂×C₄²×C₅	—	2	2	no	—
102	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
103	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
104	C₂×C₄²×C₅	D₄	1	4	yes	—
105	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
106	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
107	C₂×C₄²×C₅	C₂³	1	4	yes	—
108	C₅×#107	C₂³	1	16	yes	—
109	C₅×#103	C₂³	1	16	yes	—
110	C₅×#102	C₂³	1	16	yes	—
111	C₅×#97	C₂³	1	8	yes	—
112	C₄×C₅×C₈	C₂³	1	4	yes	—
113	C₄×C₅×C₈	C₂³	1	4	yes	—
114	C₂×#533	C₂×C₅	1	1	yes	characteristic, complemented
115	C₂×#532	C₂×C₅	1	1	yes	characteristic
116	#3182	C₂×C₅	1	16	yes	direct product factor
117	C₂×#500	C₂×C₅	1	1	yes	characteristic, complemented
118	C₂×#492	C₂×C₅	1	1	yes	characteristic, complemented
119	C₂×#487	C₂×C₅	1	1	yes	characteristic, complemented
120	C₂×#486	C₂×C₅	1	1	yes	characteristic, complemented
121	C₂×#468	C₂×C₅	1	4	yes	complemented
122	C₂×#440	C₂×C₅	1	4	yes	complemented
123	C₂×C₄×M₁₆	C₂×C₅	1	1	yes	characteristic, complemented
124	C₂⁴×C₅	—	2	2	no	—
125	C₂⁴×C₅	C₂×D₄	1	1	yes	characteristic
126	C₅×#41	—	4	32	no	—
127	C₂×C₅×Q₈	—	2	2	no	—
128	C₂×C₅×Q₈	—	2	4	no	—
129	C₂×C₅×Q₈	—	2	4	no	—
130	C₂×C₅×Q₈	—	2	8	no	—
131	C₂×C₅×Q₈	—	4	4	no	—
132	C₂×C₅×Q₈	—	4	4	no	—
133	C₂×C₅×Q₈	C₂⁴	1	4	yes	—
134	C₂×C₅×D₄	—	2	8	no	—
135	C₂×C₅×D₄	—	2	2	no	—
136	C₂×C₅×D₄	—	2	4	no	—
137	C₂×C₅×D₄	—	2	4	no	—
138	C₂×C₅×D₄	—	2	8	no	—
139	C₂×C₅×D₄	—	4	8	no	—
140	C₂×C₅×D₄	—	4	4	no	—
141	C₂×C₅×D₄	—	4	4	no	—
142	C₂×C₅×D₄	C₂⁴	1	4	yes	—
143	C₂²×C₄×C₅	—	2	4	no	—
144	C₂²×C₄×C₅	—	2	4	no	—
145	C₂²×C₄×C₅	—	2	4	no	—
146	C₂²×C₄×C₅	—	2	2	no	—
147	C₂²×C₄×C₅	—	2	2	no	—
148	C₂²×C₄×C₅	—	2	2	no	—
149	C₂²×C₄×C₅	—	2	8	no	—
150	C₂²×C₄×C₅	—	4	8	no	—
151	C₂²×C₄×C₅	C₂×D₄	1	2	yes	—
152	C₂²×C₄×C₅	C₂×D₄	1	4	yes	—
153	C₂²×C₄×C₅	C₂×D₄	1	4	yes	—
154	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
155	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
156	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
157	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
158	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
159	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
160	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
161	C₅×SD₁₆	—	2	32	no	—
162	C₅×M₁₆	—	2	16	no	—
163	C₂×C₅×C₈	—	2	4	no	—
164	C₂×C₅×C₈	#41	1	8	yes	complemented
165	C₂×C₅×C₈	C₂⁴	1	4	yes	—
166	C₂×C₅×C₈	C₂⁴	1	4	yes	—
167	C₅×C₄⋊C₄	—	2	4	no	—
168	C₅×C₄⋊C₄	—	2	4	no	—
169	C₅×C₄⋊C₄	—	2	4	no	—
170	C₅×C₄⋊C₄	—	2	4	no	—
171	C₅×C₄⋊C₄	—	2	8	no	—
172	C₅×C₄⋊C₄	—	2	8	no	—
173	C₅×C₄⋊C₄	—	2	2	no	—
174	C₅×C₄⋊C₄	—	2	2	no	—
175	C₅×C₄⋊C₄	C₂⁴	1	4	yes	—
176	C₅×C₄⋊C₄	C₂⁴	1	4	yes	—
177	C₅×C₂²⋊C₄	—	2	8	no	—
178	C₅×C₂²⋊C₄	—	2	8	no	—
179	C₅×C₂²⋊C₄	—	2	8	no	—
180	C₄²×C₅	—	2	8	no	—
181	C₄²×C₅	C₂×D₄	1	2	yes	—
182	C₄²×C₅	C₂×D₄	1	4	yes	—
183	C₄²×C₅	C₂×D₄	1	4	yes	—
184	C₄²×C₅	C₂×D₄	1	2	yes	—
185	C₄²×C₅	C₂⁴	1	2	yes	—
186	C₄²×C₅	C₂⁴	1	2	yes	—
187	C₂²×#41	—	2	1	no	—
188	C₂²×SD₁₆	C₂²×C₅	1	4	yes	—
189	C₂²×M₁₆	C₂²×C₅	1	2	yes	—
190	#533	—	2	4	no	—
191	#533	C₂²×C₅	1	8	yes	complemented
192	#532	—	2	4	no	—
193	#532	C₂²×C₅	1	8	yes	—
194	C₂×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
195	C₂×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
196	C₂×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
197	C₂×#127	C₂²×C₅	1	1	yes	characteristic
198	C₂×#125	—	2	1	no	—
199	C₂×#124	—	2	1	no	—
200	C₂×C₂²⋊Q₈	—	2	1	no	—
201	C₂×C₂²⋊Q₈	C₂²×C₅	1	2	yes	—
202	C₂×#121	—	2	1	no	—
203	C₂×#121	C₂²×C₅	1	2	yes	—
204	C₂×C₄×Q₈	—	2	1	no	—
205	C₂×C₄×Q₈	C₂²×C₅	1	2	yes	—
206	C₂×C₄×D₄	—	2	1	no	—
207	C₂×C₄×D₄	C₂²×C₅	1	2	yes	—
208	C₂×#117	—	2	1	no	—
209	C₂²×C₄²	C₂²×C₅	1	1	yes	characteristic
210	#500	C₂²×C₅	1	8	yes	complemented
211	#492	C₂²×C₅	1	8	yes	complemented
212	#487	C₂²×C₅	1	8	yes	complemented
213	#486	C₂²×C₅	1	8	yes	complemented
214	#468	C₂²×C₅	1	32	yes	complemented
215	#440	C₂²×C₅	1	32	yes	complemented
216	C₂×#107	C₂²×C₅	1	4	yes	—
217	C₂×#103	C₂²×C₅	1	4	yes	—
218	C₂×#102	C₂²×C₅	1	4	yes	—
219	C₄×M₁₆	C₂²×C₅	1	8	yes	complemented
220	C₂×#97	C₂²×C₅	1	2	yes	—
221	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
222	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
223	C₂³×C₅	—	2	2	no	—
224	C₂³×C₅	—	2	2	no	—
225	C₂³×C₅	—	2	2	no	—
226	C₂³×C₅	—	2	4	no	—
227	C₂³×C₅	—	4	4	no	—
228	C₂³×C₅	—	4	4	no	—
229	C₂³×C₅	—	4	4	no	—
230	C₂³×C₅	C₂²×D₄	1	2	yes	—
231	C₂³×C₅	C₂²×D₄	1	1	yes	characteristic
232	C₅×Q₈	—	2	8	no	—
233	C₅×Q₈	—	4	4	no	—
234	C₅×Q₈	—	4	8	no	—
235	C₅×Q₈	—	4	8	no	—
236	C₅×D₄	—	2	8	no	—
237	C₅×D₄	—	4	16	no	—
238	C₅×D₄	—	4	4	no	—
239	C₅×D₄	—	4	8	no	—
240	C₅×D₄	—	4	8	no	—
241	C₂×C₄×C₅	—	2	2	no	—
242	C₂×C₄×C₅	—	2	2	no	—
243	C₂×C₄×C₅	—	2	2	no	—
244	C₂×C₄×C₅	—	2	4	no	—
245	C₂×C₄×C₅	—	2	8	no	—
246	C₂×C₄×C₅	—	2	8	no	—
247	C₂×C₄×C₅	—	2	4	no	—
248	C₂×C₄×C₅	—	2	4	no	—
249	C₂×C₄×C₅	—	2	4	no	—
250	C₂×C₄×C₅	—	2	4	no	—
251	C₂×C₄×C₅	—	4	16	no	—
252	C₂×C₄×C₅	—	4	4	no	—
253	C₂×C₄×C₅	—	4	4	no	—
254	C₂×C₄×C₅	—	4	4	no	—
255	C₂×C₄×C₅	AGL(1,ℤ/8)	1	4	yes	—
256	C₂×C₄×C₅	#137	1	4	yes	—
257	C₂×C₄×C₅	C₂²×D₄	1	2	yes	—
258	C₂×C₄×C₅	C₂²×D₄	1	2	yes	—
259	C₂×C₄×C₅	C₂²×D₄	1	2	yes	—
260	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
261	C₂×C₄×C₅	C₂²×D₄	1	2	yes	—
262	C₂×C₄×C₅	C₂²×D₄	1	2	yes	—
263	C₂×C₄×C₅	C₂×#41	1	4	yes	—
264	C₂×C₄×C₅	C₂⁵	1	1	yes	characteristic
265	C₅×C₈	—	2	4	no	—
266	C₅×C₈	C₂×#41	1	8	yes	complemented
267	C₂×#41	—	2	8	no	—
268	C₂×#41	—	4	8	no	—
269	C₂²×Q₈	—	2	1	no	—
270	C₂²×Q₈	—	2	1	no	—
271	C₂²×Q₈	C₂³×C₅	1	2	yes	—
272	C₂²×D₄	—	2	2	no	—
273	C₂²×D₄	—	2	1	no	—
274	C₂²×D₄	—	2	1	no	—
275	C₂²×D₄	C₂³×C₅	1	2	yes	—
276	C₂³×C₄	—	2	2	no	—
277	C₂³×C₄	C₅×D₄	1	1	yes	characteristic
278	C₂³×C₄	C₅×D₄	1	1	yes	characteristic
279	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
280	C₂×SD₁₆	—	2	16	no	—
281	C₂×SD₁₆	C₂³×C₅	1	16	yes	—
282	C₂×M₁₆	—	2	8	no	—
283	C₂×M₁₆	C₂³×C₅	1	8	yes	—
284	C₂²×C₈	C₂³×C₅	1	2	yes	—
285	C₂²×C₈	C₂³×C₅	1	2	yes	—
286	C₄⋊Q₈	—	2	2	no	—
287	C₄⋊Q₈	—	2	2	no	—
288	C₄⋊Q₈	—	2	2	no	—
289	C₄⋊Q₈	C₂³×C₅	1	4	yes	—
290	C₄⋊Q₈	C₂³×C₅	1	4	yes	—
291	C₄⋊Q₈	C₂³×C₅	1	4	yes	—
292	#127	—	2	2	no	—
293	#127	C₂³×C₅	1	4	yes	—
294	#125	—	2	8	no	—
295	#124	—	2	8	no	—
296	C₂²⋊Q₈	—	2	8	no	—
297	C₂²⋊Q₈	—	2	4	no	—
298	C₂²⋊Q₈	C₂³×C₅	1	8	yes	—
299	#121	—	2	8	no	—
300	#121	—	2	4	no	—
301	#121	C₂³×C₅	1	8	yes	—
302	C₄×Q₈	—	2	8	no	—
303	C₄×Q₈	—	2	4	no	—
304	C₄×Q₈	C₂³×C₅	1	8	yes	—
305	C₄×D₄	—	2	8	no	—
306	C₄×D₄	—	2	4	no	—
307	C₄×D₄	C₂³×C₅	1	8	yes	—
308	#117	—	2	8	no	—
309	C₂×C₄⋊C₄	—	2	1	no	—
310	C₂×C₄⋊C₄	—	2	1	no	—
311	C₂×C₄⋊C₄	—	2	1	no	—
312	C₂×C₄⋊C₄	—	2	1	no	—
313	C₂×C₄⋊C₄	—	2	2	no	—
314	C₂×C₄⋊C₄	—	2	2	no	—
315	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
316	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
317	C₂×C₂²⋊C₄	—	2	2	no	—
318	C₂×C₂²⋊C₄	—	2	2	no	—
319	C₂×C₂²⋊C₄	—	2	2	no	—
320	C₂×C₄²	—	2	2	no	—
321	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
322	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
323	C₂×C₄²	C₅×D₄	1	4	yes	—
324	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
325	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
326	C₂×C₄²	C₂³×C₅	1	4	yes	—
327	#107	C₂³×C₅	1	16	yes	—
328	#103	C₂³×C₅	1	16	yes	—
329	#102	C₂³×C₅	1	16	yes	—
330	#97	C₂³×C₅	1	8	yes	—
331	C₄×C₈	C₂³×C₅	1	4	yes	—
332	C₄×C₈	C₂³×C₅	1	4	yes	—
333	C₂²×C₅	—	2	2	no	—
334	C₂²×C₅	—	2	2	no	—
335	C₂²×C₅	—	2	2	no	—
336	C₂²×C₅	—	4	4	no	—
337	C₂²×C₅	—	4	4	no	—
338	C₂²×C₅	—	4	4	no	—
339	C₂²×C₅	—	4	4	no	—
340	C₂²×C₅	—	8	8	no	—
341	C₂²×C₅	#532	1	2	yes	—
342	C₂²×C₅	C₂×AGL(1,ℤ/8)	1	2	yes	—
343	C₂²×C₅	C₂×#137	1	2	yes	—
344	C₂²×C₅	C₂³×D₄	1	1	yes	characteristic
345	C₄×C₅	—	2	2	no	—
346	C₄×C₅	—	2	2	no	—
347	C₄×C₅	—	2	2	no	—
348	C₄×C₅	—	4	4	no	—
349	C₄×C₅	—	4	4	no	—
350	C₄×C₅	—	4	4	no	—
351	C₄×C₅	#532	1	2	yes	—
352	C₄×C₅	C₂×AGL(1,ℤ/8)	1	4	yes	—
353	C₄×C₅	C₂×#137	1	4	yes	—
354	C₄×C₅	C₂²×#41	1	2	yes	—
355	C₂⁴	—	2	2	no	—
356	C₂⁴	C₂×C₅×D₄	1	1	yes	characteristic
357	#41	—	4	32	no	—
358	C₂×Q₈	—	2	2	no	—
359	C₂×Q₈	—	2	4	no	—
360	C₂×Q₈	—	2	4	no	—
361	C₂×Q₈	—	2	8	no	—
362	C₂×Q₈	—	4	4	no	—
363	C₂×Q₈	—	4	4	no	—
364	C₂×Q₈	C₂⁴×C₅	1	4	yes	—
365	C₂×D₄	—	2	8	no	—
366	C₂×D₄	—	2	2	no	—
367	C₂×D₄	—	2	4	no	—
368	C₂×D₄	—	2	4	no	—
369	C₂×D₄	—	2	8	no	—
370	C₂×D₄	—	4	8	no	—
371	C₂×D₄	—	4	4	no	—
372	C₂×D₄	—	4	4	no	—
373	C₂×D₄	C₂⁴×C₅	1	4	yes	—
374	C₂²×C₄	—	2	4	no	—
375	C₂²×C₄	—	2	4	no	—
376	C₂²×C₄	—	2	4	no	—
377	C₂²×C₄	—	2	2	no	—
378	C₂²×C₄	—	2	2	no	—
379	C₂²×C₄	—	2	2	no	—
380	C₂²×C₄	—	2	8	no	—
381	C₂²×C₄	—	4	8	no	—
382	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
383	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
384	C₂²×C₄	C₂×C₅×D₄	1	2	yes	—
385	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
386	C₂²×C₄	C₂×C₅×D₄	1	4	yes	—
387	C₂²×C₄	C₂×C₅×D₄	1	4	yes	—
388	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
389	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
390	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
391	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
392	SD₁₆	—	2	32	no	—
393	M₁₆	—	2	16	no	—
394	C₂×C₈	—	2	4	no	—
395	C₂×C₈	C₅×#41	1	8	yes	complemented
396	C₂×C₈	C₂⁴×C₅	1	4	yes	—
397	C₂×C₈	C₂⁴×C₅	1	4	yes	—
398	C₄⋊C₄	—	2	4	no	—
399	C₄⋊C₄	—	2	4	no	—
400	C₄⋊C₄	—	2	4	no	—
401	C₄⋊C₄	—	2	4	no	—
402	C₄⋊C₄	—	2	8	no	—
403	C₄⋊C₄	—	2	8	no	—
404	C₄⋊C₄	—	2	2	no	—
405	C₄⋊C₄	—	2	2	no	—
406	C₄⋊C₄	C₂⁴×C₅	1	4	yes	—
407	C₄⋊C₄	C₂⁴×C₅	1	4	yes	—
408	C₂²⋊C₄	—	2	8	no	—
409	C₂²⋊C₄	—	2	8	no	—
410	C₂²⋊C₄	—	2	8	no	—
411	C₄²	—	2	8	no	—
412	C₄²	C₂×C₅×D₄	1	2	yes	—
413	C₄²	C₂×C₅×D₄	1	4	yes	—
414	C₄²	C₂×C₅×D₄	1	4	yes	—
415	C₄²	C₂×C₅×D₄	1	2	yes	—
416	C₄²	C₂⁴×C₅	1	2	yes	—
417	C₄²	C₂⁴×C₅	1	2	yes	—
418	C₂×C₅	—	4	2	no	—
419	C₂×C₅	—	8	4	no	—
420	C₂×C₅	#3182	1	4	yes	direct product factor
421	C₂×C₅	C₂×#532	1	1	yes	characteristic
422	C₂×C₅	C₂²×AGL(1,ℤ/8)	1	1	yes	characteristic
423	C₂×C₅	C₂²×#137	1	1	yes	characteristic
424	C₂³	—	2	2	no	—
425	C₂³	—	2	2	no	—
426	C₂³	—	2	2	no	—
427	C₂³	—	2	4	no	—
428	C₂³	—	4	4	no	—
429	C₂³	—	4	4	no	—
430	C₂³	—	4	4	no	—
431	C₂³	C₂²×C₅×D₄	1	2	yes	—
432	C₂³	C₂²×C₅×D₄	1	1	yes	characteristic
433	Q₈	—	2	8	no	—
434	Q₈	—	4	4	no	—
435	Q₈	—	4	8	no	—
436	Q₈	—	4	8	no	—
437	D₄	—	2	8	no	—
438	D₄	—	4	16	no	—
439	D₄	—	4	4	no	—
440	D₄	—	4	8	no	—
441	D₄	—	4	8	no	—
442	C₂×C₄	—	2	2	no	—
443	C₂×C₄	—	2	2	no	—
444	C₂×C₄	—	2	2	no	—
445	C₂×C₄	—	2	4	no	—
446	C₂×C₄	—	2	8	no	—
447	C₂×C₄	—	2	8	no	—
448	C₂×C₄	—	2	4	no	—
449	C₂×C₄	—	2	4	no	—
450	C₂×C₄	—	2	4	no	—
451	C₂×C₄	—	2	4	no	—
452	C₂×C₄	—	4	16	no	—
453	C₂×C₄	—	4	4	no	—
454	C₂×C₄	—	4	4	no	—
455	C₂×C₄	—	4	4	no	—
456	C₂×C₄	C₅×AGL(1,ℤ/8)	1	4	yes	—
457	C₂×C₄	C₅×#137	1	4	yes	—
458	C₂×C₄	C₂²×C₅×D₄	1	2	yes	—
459	C₂×C₄	C₂²×C₅×D₄	1	2	yes	—
460	C₂×C₄	C₂²×C₅×D₄	1	2	yes	—
461	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
462	C₂×C₄	C₂²×C₅×D₄	1	2	yes	—
463	C₂×C₄	C₂²×C₅×D₄	1	2	yes	—
464	C₂×C₄	C₂×C₅×#41	1	4	yes	—
465	C₂×C₄	C₂⁵×C₅	1	1	yes	characteristic
466	C₈	—	2	4	no	—
467	C₈	C₂×C₅×#41	1	8	yes	complemented
468	C₅	C₂×#3182	1	1	yes	characteristic, direct product factor, Sylow
469	C₂²	—	2	2	no	—
470	C₂²	—	2	2	no	—
471	C₂²	—	2	2	no	—
472	C₂²	—	4	4	no	—
473	C₂²	—	4	4	no	—
474	C₂²	—	4	4	no	—
475	C₂²	—	4	4	no	—
476	C₂²	—	8	8	no	—
477	C₂²	C₅×#532	1	2	yes	—
478	C₂²	C₂×C₅×AGL(1,ℤ/8)	1	2	yes	—
479	C₂²	C₂×C₅×#137	1	2	yes	—
480	C₂²	C₂³×C₅×D₄	1	1	yes	characteristic
481	C₄	—	2	2	no	—
482	C₄	—	2	2	no	—
483	C₄	—	2	2	no	—
484	C₄	—	4	4	no	—
485	C₄	—	4	4	no	—
486	C₄	—	4	4	no	—
487	C₄	C₅×#532	1	2	yes	—
488	C₄	C₂×C₅×AGL(1,ℤ/8)	1	4	yes	—
489	C₄	C₂×C₅×#137	1	4	yes	—
490	C₄	C₂²×C₅×#41	1	2	yes	—
491	C₂	—	4	2	no	—
492	C₂	—	8	4	no	—
493	C₂	C₅×#3182	1	4	yes	direct product factor
494	C₂	C₂×C₅×#532	1	1	yes	characteristic
495	C₂	C₂²×C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
496	C₂	C₂²×C₅×#137	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₅	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₅
prime radical	C₂×C₅×#532	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₅ ◁ C₂²×C₄²×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₅×#533	C₂	semidirect
3. C₅×#3182	C₂	direct (N × H)
4. C₂×C₅×#500	C₂	semidirect
5. C₂×C₅×#492	C₂	semidirect
6. C₂×C₅×#487	C₂	semidirect
7. C₂×C₅×#486	C₂	semidirect
8. C₂×C₅×#468	C₂	semidirect
9. C₂×C₅×#440	C₂	semidirect
10. C₂×C₄×C₅×M₁₆	C₂	semidirect
15. C₅×#533	C₂²	semidirect
34. C₅×#500	C₂²	semidirect
35. C₅×#492	C₂²	semidirect
36. C₅×#487	C₂²	semidirect
37. C₅×#486	C₂²	semidirect
38. C₅×#468	C₂²	semidirect
39. C₅×#440	C₂²	semidirect
43. C₄×C₅×M₁₆	C₂²	semidirect
47. C₂×#3182	C₅	direct (N × H)
114. C₂×#533	C₂×C₅	semidirect
116. #3182	C₂×C₅	direct (N × H)
117. C₂×#500	C₂×C₅	semidirect
118. C₂×#492	C₂×C₅	semidirect
119. C₂×#487	C₂×C₅	semidirect
120. C₂×#486	C₂×C₅	semidirect
121. C₂×#468	C₂×C₅	semidirect
122. C₂×#440	C₂×C₅	semidirect
123. C₂×C₄×M₁₆	C₂×C₅	semidirect
164. C₂×C₅×C₈	#41	semidirect
191. #533	C₂²×C₅	semidirect
210. #500	C₂²×C₅	semidirect
211. #492	C₂²×C₅	semidirect
212. #487	C₂²×C₅	semidirect
213. #486	C₂²×C₅	semidirect
214. #468	C₂²×C₅	semidirect
215. #440	C₂²×C₅	semidirect
219. C₄×M₁₆	C₂²×C₅	semidirect
266. C₅×C₈	C₂×#41	semidirect
395. C₂×C₈	C₅×#41	semidirect
420. C₂×C₅	#3182	direct (N × H)
467. C₈	C₂×C₅×#41	semidirect
468. C₅	C₂×#3182	direct (N × H)
493. C₂	C₅×#3182	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
C₂×C₅×#532	2
C₅×#3182	2
C₂×C₅×#500	2
C₂×C₅×#492	2
C₂×C₅×#487	2
C₂×C₅×#486	2
C₂×C₅×#468	2
C₂×C₅×#440	2
C₂×C₄×C₅×M₁₆	2
C₂×#3182	5

Subgroups — C2×C5×#3182 #11983409

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×#3182 #11983409