Subgroups — C₂×C₅×#1586 #11940586

Order 1280.

838 conjugacy classes of subgroups.

The subgroup lattice has 406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×C₅×D₈	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅×#436	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅×C₈×D₄	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#1586	C₂	1	8	yes	maximal, direct product factor
5	C₂×C₅×#334	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₅×D₄⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₅×D₄⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₅×#322	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×C₅×D₈	C₄	1	1	yes	characteristic
10	C₂²×C₅×M₁₆	—	2	1	no	—
11	C₂³×C₅×C₈	—	2	1	no	—
12	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
13	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
14	C₄×C₅×D₈	C₄	1	4	yes	—
15	C₄×C₅×D₈	C₂²	1	4	yes	—
16	C₅×#436	—	2	2	no	—
17	C₅×#436	C₂²	1	4	yes	complemented
18	C₅×C₈×D₄	—	2	2	no	—
19	C₅×C₈×D₄	C₂²	1	4	yes	complemented
20	C₂×C₅×#107	C₄	1	1	yes	characteristic
21	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
22	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
23	C₂×C₅×#102	C₄	1	1	yes	characteristic
24	C₂×C₅×#102	C₄	1	1	yes	characteristic
25	C₂×C₅×C₂²⋊C₈	—	2	1	no	—
26	C₂×C₅×C₂²⋊C₈	—	2	1	no	—
27	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
28	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
29	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
30	C₅×#334	C₂²	1	4	yes	complemented
31	C₅×D₄⋊C₈	C₂²	1	4	yes	complemented
32	C₅×D₄⋊C₈	C₂²	1	4	yes	complemented
33	C₅×#322	C₂²	1	4	yes	complemented
34	C₂×#1586	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
35	C₂²×C₅×D₄	C₂×C₄	1	1	yes	characteristic
36	C₂²×C₅×D₄	C₂×C₄	1	1	yes	characteristic
37	C₂³×C₄×C₅	—	2	1	no	—
38	C₂³×C₄×C₅	—	2	1	no	—
39	C₂×C₅×D₈	—	2	4	no	—
40	C₂×C₅×D₈	C₂×C₄	1	4	yes	—
41	C₂×C₅×M₁₆	—	2	4	no	—
42	C₂×C₅×M₁₆	—	4	4	no	—
43	C₂²×C₅×C₈	—	2	1	no	—
44	C₂²×C₅×C₈	—	2	1	no	—
45	C₂²×C₅×C₈	—	2	1	no	—
46	C₂²×C₅×C₈	—	2	4	no	—
47	C₂²×C₅×C₈	—	4	4	no	—
48	C₂²×C₅×C₈	C₂×C₄	1	1	yes	characteristic
49	C₂²×C₅×C₈	C₂×C₄	1	1	yes	characteristic
50	C₂²×C₅×C₈	D₄	1	1	yes	characteristic
51	C₂²×C₅×C₈	D₄	1	1	yes	characteristic
52	C₄×C₅×D₄	—	2	1	no	—
53	C₄×C₅×D₄	—	2	1	no	—
54	C₄×C₅×D₄	—	2	1	no	—
55	C₄×C₅×D₄	—	2	1	no	—
56	C₄×C₅×D₄	C₂×C₄	1	2	yes	—
57	C₄×C₅×D₄	C₂×C₄	1	2	yes	—
58	C₄×C₅×D₄	C₂³	1	2	yes	—
59	C₄×C₅×D₄	C₂³	1	2	yes	—
60	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
61	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
62	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
63	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
64	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
65	C₅×#107	C₂×C₄	1	4	yes	—
66	C₅×C₄⋊C₈	—	2	1	no	—
67	C₅×C₄⋊C₈	—	2	1	no	—
68	C₅×C₄⋊C₈	C₂³	1	2	yes	—
69	C₅×C₄⋊C₈	C₂³	1	2	yes	—
70	C₅×#102	C₂×C₄	1	4	yes	—
71	C₅×#102	C₂×C₄	1	4	yes	—
72	C₅×C₂²⋊C₈	—	2	4	no	—
73	C₅×C₂²⋊C₈	—	2	4	no	—
74	C₄×C₅×C₈	—	2	1	no	—
75	C₄×C₅×C₈	C₂×C₄	1	2	yes	—
76	C₄×C₅×C₈	D₄	1	2	yes	—
77	C₄×C₅×C₈	C₂³	1	2	yes	—
78	C₄×C₅×C₈	C₂³	1	2	yes	—
79	C₄×C₅×C₈	C₂³	1	2	yes	—
80	C₂×C₄×D₈	C₂×C₅	1	1	yes	characteristic
81	C₂×#436	C₂×C₅	1	1	yes	characteristic, complemented
82	C₂×C₈×D₄	C₂×C₅	1	1	yes	characteristic, complemented
83	#1586	C₂×C₅	1	8	yes	direct product factor
84	C₂×#334	C₂×C₅	1	1	yes	characteristic, complemented
85	C₂×D₄⋊C₈	C₂×C₅	1	1	yes	characteristic, complemented
86	C₂×D₄⋊C₈	C₂×C₅	1	1	yes	characteristic, complemented
87	C₂×#322	C₂×C₅	1	1	yes	characteristic, complemented
88	C₂⁴×C₅	—	2	1	no	—
89	C₂⁴×C₅	—	2	1	no	—
90	C₂×C₅×D₄	—	2	1	no	—
91	C₂×C₅×D₄	—	2	1	no	—
92	C₂×C₅×D₄	—	2	2	no	—
93	C₂×C₅×D₄	—	2	2	no	—
94	C₂×C₅×D₄	—	2	2	no	—
95	C₂×C₅×D₄	M₁₆	1	4	yes	complemented
96	C₂×C₅×D₄	C₂²×C₄	1	2	yes	—
97	C₂×C₅×D₄	C₂²×C₄	1	2	yes	—
98	C₂²×C₄×C₅	—	2	1	no	—
99	C₂²×C₄×C₅	—	2	1	no	—
100	C₂²×C₄×C₅	—	2	2	no	—
101	C₂²×C₄×C₅	—	2	2	no	—
102	C₂²×C₄×C₅	—	2	2	no	—
103	C₂²×C₄×C₅	—	2	2	no	—
104	C₂²×C₄×C₅	—	4	2	no	—
105	C₂²×C₄×C₅	—	4	2	no	—
106	C₂²×C₄×C₅	—	4	2	no	—
107	C₂²×C₄×C₅	—	4	2	no	—
108	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
109	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
110	C₂²×C₄×C₅	#41	1	1	yes	characteristic
111	C₅×D₈	—	2	8	no	—
112	C₅×M₁₆	—	4	8	no	—
113	C₂×C₅×C₈	—	2	4	no	—
114	C₂×C₅×C₈	—	2	2	no	—
115	C₂×C₅×C₈	—	2	2	no	—
116	C₂×C₅×C₈	—	2	2	no	—
117	C₂×C₅×C₈	—	2	2	no	—
118	C₂×C₅×C₈	—	2	2	no	—
119	C₂×C₅×C₈	—	2	2	no	—
120	C₂×C₅×C₈	—	2	2	no	—
121	C₂×C₅×C₈	—	4	8	no	—
122	C₂×C₅×C₈	—	4	2	no	—
123	C₂×C₅×C₈	—	4	2	no	—
124	C₂×C₅×C₈	C₂²×C₄	1	2	yes	—
125	C₂×C₅×C₈	C₂²×C₄	1	2	yes	—
126	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
127	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
128	C₅×C₄⋊C₄	—	2	1	no	—
129	C₅×C₄⋊C₄	—	2	1	no	—
130	C₅×C₄⋊C₄	C₂²×C₄	1	2	yes	—
131	C₅×C₄⋊C₄	C₂²×C₄	1	2	yes	—
132	C₅×C₂²⋊C₄	—	2	2	no	—
133	C₅×C₂²⋊C₄	—	2	2	no	—
134	C₅×C₂²⋊C₄	—	2	2	no	—
135	C₅×C₂²⋊C₄	—	2	2	no	—
136	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
137	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
138	C₄²×C₅	#41	1	1	yes	characteristic
139	C₄²×C₅	C₂⁴	1	1	yes	characteristic
140	C₂²×D₈	C₄×C₅	1	1	yes	characteristic
141	C₂²×M₁₆	—	2	1	no	—
142	C₂³×C₈	—	2	1	no	—
143	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
144	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
145	C₄×D₈	C₄×C₅	1	4	yes	—
146	C₄×D₈	C₂²×C₅	1	4	yes	—
147	#436	—	2	2	no	—
148	#436	C₂²×C₅	1	4	yes	complemented
149	C₈×D₄	—	2	2	no	—
150	C₈×D₄	C₂²×C₅	1	4	yes	complemented
151	C₂×#107	C₄×C₅	1	1	yes	characteristic
152	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
153	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
154	C₂×#102	C₄×C₅	1	1	yes	characteristic
155	C₂×#102	C₄×C₅	1	1	yes	characteristic
156	C₂×C₂²⋊C₈	—	2	1	no	—
157	C₂×C₂²⋊C₈	—	2	1	no	—
158	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
159	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
160	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
161	#334	C₂²×C₅	1	4	yes	complemented
162	D₄⋊C₈	C₂²×C₅	1	4	yes	complemented
163	D₄⋊C₈	C₂²×C₅	1	4	yes	complemented
164	#322	C₂²×C₅	1	4	yes	complemented
165	C₂³×C₅	—	2	2	no	—
166	C₂³×C₅	—	2	4	no	—
167	C₂³×C₅	—	2	2	no	—
168	C₂³×C₅	—	4	2	no	—
169	C₂³×C₅	—	4	2	no	—
170	C₂³×C₅	—	4	2	no	—
171	C₂³×C₅	—	4	2	no	—
172	C₂³×C₅	—	4	2	no	—
173	C₂³×C₅	C₄×D₄	1	1	yes	characteristic
174	C₅×D₄	—	2	2	no	—
175	C₅×D₄	—	2	2	no	—
176	C₅×D₄	—	2	2	no	—
177	C₅×D₄	—	2	4	no	—
178	C₅×D₄	—	4	2	no	—
179	C₅×D₄	C₂×M₁₆	1	4	yes	complemented
180	C₂×C₄×C₅	—	2	2	no	—
181	C₂×C₄×C₅	—	2	2	no	—
182	C₂×C₄×C₅	—	2	2	no	—
183	C₂×C₄×C₅	—	4	2	no	—
184	C₂×C₄×C₅	—	4	2	no	—
185	C₂×C₄×C₅	—	4	2	no	—
186	C₂×C₄×C₅	—	4	2	no	—
187	C₂×C₄×C₅	—	4	2	no	—
188	C₂×C₄×C₅	—	4	2	no	—
189	C₂×C₄×C₅	—	4	4	no	—
190	C₂×C₄×C₅	—	4	4	no	—
191	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
192	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
193	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
194	C₂×C₄×C₅	C₂×M₁₆	1	2	yes	—
195	C₂×C₄×C₅	#131	1	2	yes	—
196	C₂×C₄×C₅	AGL(1,ℤ/8)	1	2	yes	—
197	C₂×C₄×C₅	AGL(1,ℤ/8)	1	2	yes	—
198	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
199	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
200	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
201	C₅×C₈	—	2	4	no	—
202	C₅×C₈	—	2	2	no	—
203	C₅×C₈	—	2	2	no	—
204	C₅×C₈	—	2	2	no	—
205	C₅×C₈	—	2	2	no	—
206	C₅×C₈	—	4	2	no	—
207	C₅×C₈	—	4	2	no	—
208	C₂²×D₄	C₂×C₄×C₅	1	1	yes	characteristic
209	C₂²×D₄	C₂×C₄×C₅	1	1	yes	characteristic
210	C₂³×C₄	—	2	1	no	—
211	C₂³×C₄	—	2	1	no	—
212	C₂×D₈	—	2	4	no	—
213	C₂×D₈	C₂×C₄×C₅	1	4	yes	—
214	C₂×M₁₆	—	2	4	no	—
215	C₂×M₁₆	—	4	4	no	—
216	C₂²×C₈	—	2	1	no	—
217	C₂²×C₈	—	2	1	no	—
218	C₂²×C₈	—	2	1	no	—
219	C₂²×C₈	—	2	4	no	—
220	C₂²×C₈	—	4	4	no	—
221	C₂²×C₈	C₂×C₄×C₅	1	1	yes	characteristic
222	C₂²×C₈	C₂×C₄×C₅	1	1	yes	characteristic
223	C₂²×C₈	C₅×D₄	1	1	yes	characteristic
224	C₂²×C₈	C₅×D₄	1	1	yes	characteristic
225	C₄×D₄	—	2	1	no	—
226	C₄×D₄	—	2	1	no	—
227	C₄×D₄	—	2	1	no	—
228	C₄×D₄	—	2	1	no	—
229	C₄×D₄	C₂×C₄×C₅	1	2	yes	—
230	C₄×D₄	C₂×C₄×C₅	1	2	yes	—
231	C₄×D₄	C₂³×C₅	1	2	yes	—
232	C₄×D₄	C₂³×C₅	1	2	yes	—
233	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
234	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
235	C₂×C₂²⋊C₄	—	2	1	no	—
236	C₂×C₂²⋊C₄	—	2	1	no	—
237	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
238	#107	C₂×C₄×C₅	1	4	yes	—
239	C₄⋊C₈	—	2	1	no	—
240	C₄⋊C₈	—	2	1	no	—
241	C₄⋊C₈	C₂³×C₅	1	2	yes	—
242	C₄⋊C₈	C₂³×C₅	1	2	yes	—
243	#102	C₂×C₄×C₅	1	4	yes	—
244	#102	C₂×C₄×C₅	1	4	yes	—
245	C₂²⋊C₈	—	2	4	no	—
246	C₂²⋊C₈	—	2	4	no	—
247	C₄×C₈	—	2	1	no	—
248	C₄×C₈	C₂×C₄×C₅	1	2	yes	—
249	C₄×C₈	C₅×D₄	1	2	yes	—
250	C₄×C₈	C₂³×C₅	1	2	yes	—
251	C₄×C₈	C₂³×C₅	1	2	yes	—
252	C₄×C₈	C₂³×C₅	1	2	yes	—
253	C₂²×C₅	—	2	4	no	—
254	C₂²×C₅	—	4	8	no	—
255	C₂²×C₅	—	4	2	no	—
256	C₂²×C₅	—	4	2	no	—
257	C₂²×C₅	—	4	2	no	—
258	C₂²×C₅	—	4	2	no	—
259	C₂²×C₅	—	4	2	no	—
260	C₂²×C₅	—	8	4	no	—
261	C₂²×C₅	#435	1	2	yes	—
262	C₂²×C₅	#442	1	2	yes	—
263	C₂²×C₅	#443	1	2	yes	—
264	C₂²×C₅	C₂×C₄×D₄	1	1	yes	characteristic
265	C₄×C₅	—	2	1	no	—
266	C₄×C₅	—	2	1	no	—
267	C₄×C₅	—	4	2	no	—
268	C₄×C₅	—	4	2	no	—
269	C₄×C₅	#435	1	2	yes	—
270	C₄×C₅	#442	1	2	yes	—
271	C₄×C₅	C₂²×M₁₆	1	1	yes	characteristic
272	C₄×C₅	C₂×#131	1	1	yes	characteristic
273	C₄×C₅	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
274	C₄×C₅	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
275	C₂⁴	—	2	1	no	—
276	C₂⁴	—	2	1	no	—
277	C₂×D₄	—	2	1	no	—
278	C₂×D₄	—	2	1	no	—
279	C₂×D₄	—	2	2	no	—
280	C₂×D₄	—	2	2	no	—
281	C₂×D₄	—	2	2	no	—
282	C₂×D₄	C₅×M₁₆	1	4	yes	complemented
283	C₂×D₄	C₂²×C₄×C₅	1	2	yes	—
284	C₂×D₄	C₂²×C₄×C₅	1	2	yes	—
285	C₂²×C₄	—	2	1	no	—
286	C₂²×C₄	—	2	1	no	—
287	C₂²×C₄	—	2	2	no	—
288	C₂²×C₄	—	2	2	no	—
289	C₂²×C₄	—	2	2	no	—
290	C₂²×C₄	—	2	2	no	—
291	C₂²×C₄	—	4	2	no	—
292	C₂²×C₄	—	4	2	no	—
293	C₂²×C₄	—	4	2	no	—
294	C₂²×C₄	—	4	2	no	—
295	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
296	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
297	C₂²×C₄	C₅×#41	1	1	yes	characteristic
298	D₈	—	2	8	no	—
299	M₁₆	—	4	8	no	—
300	C₂×C₈	—	2	4	no	—
301	C₂×C₈	—	2	2	no	—
302	C₂×C₈	—	2	2	no	—
303	C₂×C₈	—	2	2	no	—
304	C₂×C₈	—	2	2	no	—
305	C₂×C₈	—	2	2	no	—
306	C₂×C₈	—	2	2	no	—
307	C₂×C₈	—	2	2	no	—
308	C₂×C₈	—	4	8	no	—
309	C₂×C₈	—	4	2	no	—
310	C₂×C₈	—	4	2	no	—
311	C₂×C₈	C₂²×C₄×C₅	1	2	yes	—
312	C₂×C₈	C₂²×C₄×C₅	1	2	yes	—
313	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
314	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
315	C₄⋊C₄	—	2	1	no	—
316	C₄⋊C₄	—	2	1	no	—
317	C₄⋊C₄	C₂²×C₄×C₅	1	2	yes	—
318	C₄⋊C₄	C₂²×C₄×C₅	1	2	yes	—
319	C₂²⋊C₄	—	2	2	no	—
320	C₂²⋊C₄	—	2	2	no	—
321	C₂²⋊C₄	—	2	2	no	—
322	C₂²⋊C₄	—	2	2	no	—
323	C₄²	C₂²×C₄×C₅	1	1	yes	characteristic
324	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
325	C₄²	C₅×#41	1	1	yes	characteristic
326	C₄²	C₂⁴×C₅	1	1	yes	characteristic
327	C₂×C₅	—	4	4	no	—
328	C₂×C₅	—	8	2	no	—
329	C₂×C₅	#1586	1	4	yes	direct product factor
330	C₂×C₅	C₂×#435	1	1	yes	characteristic
331	C₂×C₅	C₂×#442	1	1	yes	characteristic
332	C₂×C₅	C₂×#443	1	1	yes	characteristic
333	C₂³	—	2	4	no	—
334	C₂³	—	2	2	no	—
335	C₂³	—	2	2	no	—
336	C₂³	—	4	2	no	—
337	C₂³	—	4	2	no	—
338	C₂³	—	4	2	no	—
339	C₂³	—	4	2	no	—
340	C₂³	—	4	2	no	—
341	C₂³	C₄×C₅×D₄	1	1	yes	characteristic
342	D₄	—	2	4	no	—
343	D₄	—	2	2	no	—
344	D₄	—	2	2	no	—
345	D₄	—	2	2	no	—
346	D₄	—	4	2	no	—
347	D₄	C₂×C₅×M₁₆	1	4	yes	complemented
348	C₂×C₄	—	2	2	no	—
349	C₂×C₄	—	2	2	no	—
350	C₂×C₄	—	2	2	no	—
351	C₂×C₄	—	4	2	no	—
352	C₂×C₄	—	4	2	no	—
353	C₂×C₄	—	4	4	no	—
354	C₂×C₄	—	4	4	no	—
355	C₂×C₄	—	4	2	no	—
356	C₂×C₄	—	4	2	no	—
357	C₂×C₄	—	4	2	no	—
358	C₂×C₄	—	4	2	no	—
359	C₂×C₄	C₄×C₅×D₄	1	1	yes	characteristic
360	C₂×C₄	C₄×C₅×D₄	1	1	yes	characteristic
361	C₂×C₄	C₄×C₅×D₄	1	1	yes	characteristic
362	C₂×C₄	C₂×C₅×M₁₆	1	2	yes	—
363	C₂×C₄	C₅×#131	1	2	yes	—
364	C₂×C₄	C₅×AGL(1,ℤ/8)	1	2	yes	—
365	C₂×C₄	C₅×AGL(1,ℤ/8)	1	2	yes	—
366	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
367	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
368	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
369	C₈	—	2	4	no	—
370	C₈	—	2	2	no	—
371	C₈	—	2	2	no	—
372	C₈	—	2	2	no	—
373	C₈	—	2	2	no	—
374	C₈	—	4	2	no	—
375	C₈	—	4	2	no	—
376	C₅	C₂×#1586	1	1	yes	characteristic, direct product factor, Sylow
377	C₂²	—	2	4	no	—
378	C₂²	—	4	8	no	—
379	C₂²	—	4	2	no	—
380	C₂²	—	4	2	no	—
381	C₂²	—	4	2	no	—
382	C₂²	—	4	2	no	—
383	C₂²	—	4	2	no	—
384	C₂²	—	8	4	no	—
385	C₂²	C₅×#435	1	2	yes	—
386	C₂²	C₅×#442	1	2	yes	—
387	C₂²	C₅×#443	1	2	yes	—
388	C₂²	C₂×C₄×C₅×D₄	1	1	yes	characteristic
389	C₄	—	2	1	no	—
390	C₄	—	2	1	no	—
391	C₄	—	4	2	no	—
392	C₄	—	4	2	no	—
393	C₄	C₅×#435	1	2	yes	—
394	C₄	C₅×#442	1	2	yes	—
395	C₄	C₂²×C₅×M₁₆	1	1	yes	characteristic
396	C₄	C₂×C₅×#131	1	1	yes	characteristic
397	C₄	C₂×C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
398	C₄	C₂×C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
399	C₂	—	4	4	no	—
400	C₂	—	8	2	no	—
401	C₂	C₅×#1586	1	4	yes	direct product factor
402	C₂	C₂×C₅×#435	1	1	yes	characteristic
403	C₂	C₂×C₅×#442	1	1	yes	characteristic
404	C₂	C₂×C₅×#443	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₅	C₂×D₄
commutator	C₂×C₄	C₂³×C₄×C₅
Frattini, cosocle	C₄²	C₂⁴×C₅
socle	C₂³×C₅	C₄×D₄
prime radical	C₂²×C₅×D₈	C₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₅ ◁ C₂×C₄×C₅×C₈ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₅×#436	C₂	semidirect
3. C₂×C₅×C₈×D₄	C₂	semidirect
4. C₅×#1586	C₂	direct (N × H)
5. C₂×C₅×#334	C₂	semidirect
6. C₂×C₅×D₄⋊C₈	C₂	semidirect
7. C₂×C₅×D₄⋊C₈	C₂	semidirect
8. C₂×C₅×#322	C₂	semidirect
17. C₅×#436	C₂²	semidirect
19. C₅×C₈×D₄	C₂²	semidirect
30. C₅×#334	C₂²	semidirect
31. C₅×D₄⋊C₈	C₂²	semidirect
32. C₅×D₄⋊C₈	C₂²	semidirect
33. C₅×#322	C₂²	semidirect
34. C₂×#1586	C₅	direct (N × H)
81. C₂×#436	C₂×C₅	semidirect
82. C₂×C₈×D₄	C₂×C₅	semidirect
83. #1586	C₂×C₅	direct (N × H)
84. C₂×#334	C₂×C₅	semidirect
85. C₂×D₄⋊C₈	C₂×C₅	semidirect
86. C₂×D₄⋊C₈	C₂×C₅	semidirect
87. C₂×#322	C₂×C₅	semidirect
95. C₂×C₅×D₄	M₁₆	semidirect
148. #436	C₂²×C₅	semidirect
150. C₈×D₄	C₂²×C₅	semidirect
161. #334	C₂²×C₅	semidirect
162. D₄⋊C₈	C₂²×C₅	semidirect
163. D₄⋊C₈	C₂²×C₅	semidirect
164. #322	C₂²×C₅	semidirect
179. C₅×D₄	C₂×M₁₆	semidirect
282. C₂×D₄	C₅×M₁₆	semidirect
329. C₂×C₅	#1586	direct (N × H)
347. D₄	C₂×C₅×M₁₆	semidirect
376. C₅	C₂×#1586	direct (N × H)
401. C₂	C₅×#1586	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×C₄×C₅×D₈	2
C₂×C₅×#436	2
C₂×C₅×C₈×D₄	2
C₅×#1586	2
C₂×C₅×#334	2
C₂×C₅×D₄⋊C₈	2
C₂×C₅×#322	2
C₂×#1586	5

Subgroups — C2×C5×#1586 #11940586

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×#1586 #11940586