Subgroups — C₅×#21682 #11944402

Order 1280.

1230 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#436	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₅×#435	C₂	1	4	yes	maximal, complemented
3	C₂×C₅×C₈×D₄	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄×C₅×#127	C₂	1	1	yes	maximal, characteristic
5	C₅×#1955	C₂	1	4	yes	maximal, complemented
6	C₅×#1954	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#1954	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#1842	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄×C₅×#97	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×C₅×M₁₆	C₂²	1	2	yes	—
11	C₂³×C₅×C₈	C₂²	1	2	yes	—
12	C₂×C₅×#127	C₄	1	1	yes	characteristic
13	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
14	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
15	C₂×C₄×C₅×D₄	C₂²	1	4	yes	—
16	C₅×#436	—	2	4	no	—
17	C₅×#435	—	2	16	no	—
18	C₅×C₈×D₄	—	2	4	no	—
19	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
20	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
21	C₂×C₅×C₄⋊C₈	C₂²	1	4	yes	—
22	C₂×C₅×C₂²⋊C₈	C₂²	1	4	yes	—
23	C₂×C₅×C₂²⋊C₈	C₂²	1	4	yes	—
24	C₂×C₅×C₂²⋊C₈	C₂²	1	2	yes	—
25	C₂×C₅×C₂²⋊C₈	C₂²	1	2	yes	—
26	C₂×C₅×#97	C₂²	1	2	yes	—
27	C₂×C₅×#97	C₂²	1	2	yes	—
28	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
29	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
30	C₅×#390	C₄	1	1	yes	characteristic
31	C₅×#390	C₄	1	1	yes	characteristic
32	C₅×#390	C₄	1	4	yes	—
33	C₅×#384	C₄	1	1	yes	characteristic
34	C₄³×C₅	C₂²	1	1	yes	characteristic
35	#21682	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
36	C₂²×C₅×D₄	C₂×C₄	1	1	yes	characteristic
37	C₂²×C₅×D₄	C₂×C₄	1	4	yes	—
38	C₂²×C₅×D₄	C₂×C₄	1	1	yes	characteristic
39	C₂³×C₄×C₅	C₂³	1	2	yes	—
40	C₂³×C₄×C₅	C₂³	1	2	yes	—
41	C₂×C₅×M₁₆	—	2	8	no	—
42	C₂×C₅×M₁₆	—	2	4	no	—
43	C₂²×C₅×C₈	—	2	4	no	—
44	C₂²×C₅×C₈	—	2	8	no	—
45	C₂²×C₅×C₈	C₂³	1	2	yes	—
46	C₂²×C₅×C₈	C₂³	1	2	yes	—
47	C₂²×C₅×C₈	C₂³	1	2	yes	—
48	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
49	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
50	C₅×#127	—	2	4	no	—
51	C₄×C₅×D₄	—	2	2	no	—
52	C₄×C₅×D₄	—	2	8	no	—
53	C₄×C₅×D₄	—	2	2	no	—
54	C₄×C₅×D₄	—	2	2	no	—
55	C₄×C₅×D₄	—	2	2	no	—
56	C₄×C₅×D₄	—	2	8	no	—
57	C₂×C₅×C₄⋊C₄	C₂×C₄	1	4	yes	—
58	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
59	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
60	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	2	yes	—
61	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	4	yes	—
62	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	2	yes	—
63	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	4	yes	—
64	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
65	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
66	C₂×C₄²×C₅	C₂×C₄	1	2	yes	—
67	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
68	C₂×C₄²×C₅	C₂³	1	2	yes	—
69	C₅×C₄⋊C₈	—	2	2	no	—
70	C₅×C₄⋊C₈	—	2	8	no	—
71	C₅×C₄⋊C₈	—	2	2	no	—
72	C₅×C₂²⋊C₈	—	2	4	no	—
73	C₅×C₂²⋊C₈	—	2	8	no	—
74	C₅×C₂²⋊C₈	—	2	8	no	—
75	C₅×C₂²⋊C₈	—	2	4	no	—
76	C₅×#97	—	2	4	no	—
77	C₅×#97	D₄	1	8	yes	complemented
78	C₄×C₅×C₈	—	2	2	no	—
79	C₄×C₅×C₈	D₄	1	4	yes	complemented
80	C₂×#436	C₂×C₅	1	1	yes	characteristic, complemented
81	C₂×#435	C₂×C₅	1	4	yes	complemented
82	C₂×C₈×D₄	C₂×C₅	1	1	yes	characteristic, complemented
83	C₄×#127	C₂×C₅	1	1	yes	characteristic
84	#1955	C₂×C₅	1	4	yes	complemented
85	#1954	C₂×C₅	1	1	yes	characteristic, complemented
86	#1954	C₂×C₅	1	1	yes	characteristic, complemented
87	#1842	C₂×C₅	1	1	yes	characteristic, complemented
88	C₄×#97	C₂×C₅	1	1	yes	characteristic, complemented
89	C₂⁴×C₅	C₂²×C₄	1	2	yes	—
90	C₂⁴×C₅	C₂²×C₄	1	2	yes	—
91	C₂×C₅×D₄	—	2	8	no	—
92	C₂×C₅×D₄	—	2	2	no	—
93	C₂×C₅×D₄	—	2	8	no	—
94	C₂×C₅×D₄	—	2	2	no	—
95	C₂×C₅×D₄	—	2	2	no	—
96	C₂×C₅×D₄	—	2	2	no	—
97	C₂×C₅×D₄	—	2	2	no	—
98	C₂×C₅×D₄	—	4	4	no	—
99	C₂×C₅×D₄	M₁₆	1	4	yes	complemented
100	C₂²×C₄×C₅	—	2	2	no	—
101	C₂²×C₄×C₅	—	2	4	no	—
102	C₂²×C₄×C₅	—	2	4	no	—
103	C₂²×C₄×C₅	—	2	2	no	—
104	C₂²×C₄×C₅	—	2	2	no	—
105	C₂²×C₄×C₅	—	2	4	no	—
106	C₂²×C₄×C₅	—	2	2	no	—
107	C₂²×C₄×C₅	—	2	4	no	—
108	C₂²×C₄×C₅	C₂²×C₄	1	2	yes	—
109	C₂²×C₄×C₅	C₂²×C₄	1	2	yes	—
110	C₂²×C₄×C₅	C₂²×C₄	1	2	yes	—
111	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
112	C₂²×C₄×C₅	C₂²×C₄	1	2	yes	—
113	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
114	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
115	C₅×M₁₆	—	4	8	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	4	no	—
121	C₂×C₅×C₈	—	2	4	no	—
122	C₂×C₅×C₈	—	2	2	no	—
123	C₂×C₅×C₈	—	4	8	no	—
124	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
125	C₂×C₅×C₈	C₂×D₄	1	4	yes	—
126	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
127	C₂×C₅×C₈	C₂×D₄	1	4	yes	—
128	C₅×C₄⋊C₄	—	2	8	no	—
129	C₅×C₄⋊C₄	—	2	2	no	—
130	C₅×C₄⋊C₄	—	2	2	no	—
131	C₅×C₂²⋊C₄	—	2	4	no	—
132	C₅×C₂²⋊C₄	—	2	8	no	—
133	C₅×C₂²⋊C₄	—	2	8	no	—
134	C₅×C₂²⋊C₄	—	2	4	no	—
135	C₄²×C₅	—	2	2	no	—
136	C₄²×C₅	—	2	2	no	—
137	C₄²×C₅	—	4	2	no	—
138	C₄²×C₅	C₂×D₄	1	2	yes	—
139	C₄²×C₅	C₂×D₄	1	4	yes	—
140	C₄²×C₅	#41	1	2	yes	—
141	C₄²×C₅	#41	1	4	yes	—
142	C₂²×M₁₆	C₂²×C₅	1	2	yes	—
143	C₂³×C₈	C₂²×C₅	1	2	yes	—
144	C₂×#127	C₄×C₅	1	1	yes	characteristic
145	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
146	C₂×C₄×D₄	C₂²×C₅	1	4	yes	—
147	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
148	#436	—	2	4	no	—
149	#435	—	2	16	no	—
150	C₈×D₄	—	2	4	no	—
151	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
152	C₂×C₄⋊C₈	C₂²×C₅	1	4	yes	—
153	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
154	C₂×C₂²⋊C₈	C₂²×C₅	1	2	yes	—
155	C₂×C₂²⋊C₈	C₂²×C₅	1	4	yes	—
156	C₂×C₂²⋊C₈	C₂²×C₅	1	4	yes	—
157	C₂×C₂²⋊C₈	C₂²×C₅	1	2	yes	—
158	C₂×#97	C₂²×C₅	1	2	yes	—
159	C₂×#97	C₂²×C₅	1	2	yes	—
160	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
161	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
162	#390	C₄×C₅	1	1	yes	characteristic
163	#390	C₄×C₅	1	1	yes	characteristic
164	#390	C₄×C₅	1	4	yes	—
165	#384	C₄×C₅	1	1	yes	characteristic
166	C₄³	C₂²×C₅	1	1	yes	characteristic
167	C₂³×C₅	—	2	2	no	—
168	C₂³×C₅	—	2	4	no	—
169	C₂³×C₅	—	2	2	no	—
170	C₂³×C₅	—	2	4	no	—
171	C₂³×C₅	—	2	2	no	—
172	C₂³×C₅	—	2	4	no	—
173	C₂³×C₅	—	2	2	no	—
174	C₂³×C₅	—	2	2	no	—
175	C₂³×C₅	—	2	4	no	—
176	C₂³×C₅	C₂×M₁₆	1	4	yes	—
177	C₂³×C₅	C₂³×C₄	1	1	yes	characteristic
178	C₅×D₄	—	2	8	no	—
179	C₅×D₄	—	4	16	no	—
180	C₅×D₄	—	4	4	no	—
181	C₂×C₄×C₅	—	2	2	no	—
182	C₂×C₄×C₅	—	2	2	no	—
183	C₂×C₄×C₅	—	2	2	no	—
184	C₂×C₄×C₅	—	2	2	no	—
185	C₂×C₄×C₅	—	2	2	no	—
186	C₂×C₄×C₅	—	2	2	no	—
187	C₂×C₄×C₅	—	2	2	no	—
188	C₂×C₄×C₅	—	2	4	no	—
189	C₂×C₄×C₅	—	2	4	no	—
190	C₂×C₄×C₅	—	4	2	no	—
191	C₂×C₄×C₅	—	4	2	no	—
192	C₂×C₄×C₅	—	4	2	no	—
193	C₂×C₄×C₅	—	4	4	no	—
194	C₂×C₄×C₅	—	4	4	no	—
195	C₂×C₄×C₅	—	4	2	no	—
196	C₂×C₄×C₅	C₄×D₄	1	2	yes	—
197	C₂×C₄×C₅	C₄×D₄	1	4	yes	—
198	C₂×C₄×C₅	C₄×D₄	1	4	yes	—
199	C₂×C₄×C₅	C₄×D₄	1	2	yes	—
200	C₂×C₄×C₅	C₂×M₁₆	1	2	yes	—
201	C₂×C₄×C₅	#131	1	2	yes	—
202	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
203	C₂×C₄×C₅	C₂²×D₄	1	2	yes	—
204	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
205	C₂×C₄×C₅	C₂×#41	1	2	yes	—
206	C₅×C₈	—	2	4	no	—
207	C₅×C₈	—	2	2	no	—
208	C₅×C₈	—	4	2	no	—
209	C₅×C₈	—	4	2	no	—
210	C₅×C₈	#127	1	4	yes	complemented
211	C₂²×D₄	C₂×C₄×C₅	1	1	yes	characteristic
212	C₂²×D₄	C₂×C₄×C₅	1	4	yes	—
213	C₂²×D₄	C₂×C₄×C₅	1	1	yes	characteristic
214	C₂³×C₄	C₂³×C₅	1	2	yes	—
215	C₂³×C₄	C₂³×C₅	1	2	yes	—
216	C₂×M₁₆	—	2	8	no	—
217	C₂×M₁₆	—	2	4	no	—
218	C₂²×C₈	—	2	4	no	—
219	C₂²×C₈	—	2	8	no	—
220	C₂²×C₈	C₂³×C₅	1	2	yes	—
221	C₂²×C₈	C₂³×C₅	1	2	yes	—
222	C₂²×C₈	C₂³×C₅	1	2	yes	—
223	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
224	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
225	#127	—	2	4	no	—
226	C₄×D₄	—	2	2	no	—
227	C₄×D₄	—	2	8	no	—
228	C₄×D₄	—	2	2	no	—
229	C₄×D₄	—	2	2	no	—
230	C₄×D₄	—	2	2	no	—
231	C₄×D₄	—	2	8	no	—
232	C₂×C₄⋊C₄	C₂×C₄×C₅	1	4	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	C₂×C₄×C₅	1	4	yes	—
236	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	2	yes	—
237	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	2	yes	—
238	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	4	yes	—
239	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
240	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
241	C₂×C₄²	C₂×C₄×C₅	1	2	yes	—
242	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
243	C₂×C₄²	C₂³×C₅	1	2	yes	—
244	C₄⋊C₈	—	2	2	no	—
245	C₄⋊C₈	—	2	8	no	—
246	C₄⋊C₈	—	2	2	no	—
247	C₂²⋊C₈	—	2	4	no	—
248	C₂²⋊C₈	—	2	8	no	—
249	C₂²⋊C₈	—	2	8	no	—
250	C₂²⋊C₈	—	2	4	no	—
251	#97	—	2	4	no	—
252	#97	C₅×D₄	1	8	yes	complemented
253	C₄×C₈	—	2	2	no	—
254	C₄×C₈	C₅×D₄	1	4	yes	complemented
255	C₂²×C₅	—	2	4	no	—
256	C₂²×C₅	—	2	8	no	—
257	C₂²×C₅	—	4	2	no	—
258	C₂²×C₅	—	4	2	no	—
259	C₂²×C₅	—	4	4	no	—
260	C₂²×C₅	—	4	2	no	—
261	C₂²×C₅	—	4	2	no	—
262	C₂²×C₅	—	4	2	no	—
263	C₂²×C₅	—	4	4	no	—
264	C₂²×C₅	—	4	4	no	—
265	C₂²×C₅	C₂×C₄×D₄	1	1	yes	characteristic
266	C₂²×C₅	C₂×C₄×D₄	1	2	yes	—
267	C₂²×C₅	C₂²×M₁₆	1	1	yes	characteristic
268	C₂²×C₅	C₂×#131	1	1	yes	characteristic
269	C₂²×C₅	#568	1	2	yes	—
270	C₄×C₅	—	2	2	no	—
271	C₄×C₅	—	2	4	no	—
272	C₄×C₅	—	2	4	no	—
273	C₄×C₅	—	4	2	no	—
274	C₄×C₅	—	4	2	no	—
275	C₄×C₅	#435	1	4	yes	complemented
276	C₄×C₅	C₂×#127	1	1	yes	characteristic
277	C₄×C₅	#532	1	2	yes	—
278	C₄×C₅	#532	1	1	yes	characteristic
279	C₂⁴	C₂²×C₄×C₅	1	2	yes	—
280	C₂⁴	C₂²×C₄×C₅	1	2	yes	—
281	C₂×D₄	—	2	8	no	—
282	C₂×D₄	—	2	2	no	—
283	C₂×D₄	—	2	8	no	—
284	C₂×D₄	—	2	2	no	—
285	C₂×D₄	—	2	2	no	—
286	C₂×D₄	—	2	2	no	—
287	C₂×D₄	—	2	2	no	—
288	C₂×D₄	—	4	4	no	—
289	C₂×D₄	C₅×M₁₆	1	4	yes	complemented
290	C₂²×C₄	—	2	2	no	—
291	C₂²×C₄	—	2	4	no	—
292	C₂²×C₄	—	2	4	no	—
293	C₂²×C₄	—	2	2	no	—
294	C₂²×C₄	—	2	2	no	—
295	C₂²×C₄	—	2	4	no	—
296	C₂²×C₄	—	2	2	no	—
297	C₂²×C₄	—	2	4	no	—
298	C₂²×C₄	C₂²×C₄×C₅	1	2	yes	—
299	C₂²×C₄	C₂²×C₄×C₅	1	2	yes	—
300	C₂²×C₄	C₂²×C₄×C₅	1	2	yes	—
301	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
302	C₂²×C₄	C₂²×C₄×C₅	1	2	yes	—
303	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
304	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
305	M₁₆	—	4	8	no	—
306	C₂×C₈	—	2	2	no	—
307	C₂×C₈	—	2	2	no	—
308	C₂×C₈	—	2	2	no	—
309	C₂×C₈	—	2	2	no	—
310	C₂×C₈	—	2	4	no	—
311	C₂×C₈	—	2	4	no	—
312	C₂×C₈	—	2	2	no	—
313	C₂×C₈	—	4	8	no	—
314	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
315	C₂×C₈	C₂×C₅×D₄	1	4	yes	—
316	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
317	C₂×C₈	C₂×C₅×D₄	1	4	yes	—
318	C₄⋊C₄	—	2	8	no	—
319	C₄⋊C₄	—	2	2	no	—
320	C₄⋊C₄	—	2	2	no	—
321	C₂²⋊C₄	—	2	4	no	—
322	C₂²⋊C₄	—	2	8	no	—
323	C₂²⋊C₄	—	2	8	no	—
324	C₂²⋊C₄	—	2	4	no	—
325	C₄²	—	2	2	no	—
326	C₄²	—	2	2	no	—
327	C₄²	—	4	2	no	—
328	C₄²	C₂×C₅×D₄	1	2	yes	—
329	C₄²	C₂×C₅×D₄	1	4	yes	—
330	C₄²	C₅×#41	1	2	yes	—
331	C₄²	C₅×#41	1	4	yes	—
332	C₂×C₅	—	4	4	no	—
333	C₂×C₅	—	8	2	no	—
334	C₂×C₅	C₄×#127	1	1	yes	characteristic
335	C₂×C₅	C₂×#435	1	1	yes	characteristic
336	C₂×C₅	#2932	1	1	yes	characteristic
337	C₂×C₅	D₄×M₁₆	1	2	yes	—
338	C₂×C₅	#2935	1	2	yes	—
339	C₂³	—	2	2	no	—
340	C₂³	—	2	4	no	—
341	C₂³	—	2	2	no	—
342	C₂³	—	2	4	no	—
343	C₂³	—	2	2	no	—
344	C₂³	—	2	4	no	—
345	C₂³	—	2	2	no	—
346	C₂³	—	2	2	no	—
347	C₂³	—	2	4	no	—
348	C₂³	C₂×C₅×M₁₆	1	4	yes	—
349	C₂³	C₂³×C₄×C₅	1	1	yes	characteristic
350	D₄	—	2	8	no	—
351	D₄	—	4	16	no	—
352	D₄	—	4	4	no	—
353	C₂×C₄	—	2	2	no	—
354	C₂×C₄	—	2	2	no	—
355	C₂×C₄	—	2	2	no	—
356	C₂×C₄	—	2	2	no	—
357	C₂×C₄	—	2	2	no	—
358	C₂×C₄	—	2	2	no	—
359	C₂×C₄	—	2	2	no	—
360	C₂×C₄	—	2	4	no	—
361	C₂×C₄	—	2	4	no	—
362	C₂×C₄	—	4	2	no	—
363	C₂×C₄	—	4	2	no	—
364	C₂×C₄	—	4	2	no	—
365	C₂×C₄	—	4	4	no	—
366	C₂×C₄	—	4	4	no	—
367	C₂×C₄	—	4	2	no	—
368	C₂×C₄	C₄×C₅×D₄	1	2	yes	—
369	C₂×C₄	C₄×C₅×D₄	1	4	yes	—
370	C₂×C₄	C₄×C₅×D₄	1	4	yes	—
371	C₂×C₄	C₄×C₅×D₄	1	2	yes	—
372	C₂×C₄	C₂×C₅×M₁₆	1	2	yes	—
373	C₂×C₄	C₅×#131	1	2	yes	—
374	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
375	C₂×C₄	C₂²×C₅×D₄	1	2	yes	—
376	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
377	C₂×C₄	C₂×C₅×#41	1	2	yes	—
378	C₈	—	2	4	no	—
379	C₈	—	2	2	no	—
380	C₈	—	4	2	no	—
381	C₈	—	4	2	no	—
382	C₈	C₅×#127	1	4	yes	complemented
383	C₅	#21682	1	1	yes	characteristic, direct product factor, Sylow
384	C₂²	—	2	4	no	—
385	C₂²	—	2	8	no	—
386	C₂²	—	4	2	no	—
387	C₂²	—	4	2	no	—
388	C₂²	—	4	4	no	—
389	C₂²	—	4	2	no	—
390	C₂²	—	4	2	no	—
391	C₂²	—	4	2	no	—
392	C₂²	—	4	4	no	—
393	C₂²	—	4	4	no	—
394	C₂²	C₂×C₄×C₅×D₄	1	1	yes	characteristic
395	C₂²	C₂×C₄×C₅×D₄	1	2	yes	—
396	C₂²	C₂²×C₅×M₁₆	1	1	yes	characteristic
397	C₂²	C₂×C₅×#131	1	1	yes	characteristic
398	C₂²	C₅×#568	1	2	yes	—
399	C₄	—	2	2	no	—
400	C₄	—	2	4	no	—
401	C₄	—	2	4	no	—
402	C₄	—	4	2	no	—
403	C₄	—	4	2	no	—
404	C₄	C₅×#435	1	4	yes	complemented
405	C₄	C₂×C₅×#127	1	1	yes	characteristic
406	C₄	C₅×#532	1	2	yes	—
407	C₄	C₅×#532	1	1	yes	characteristic
408	C₂	—	4	4	no	—
409	C₂	—	8	2	no	—
410	C₂	C₄×C₅×#127	1	1	yes	characteristic
411	C₂	C₂×C₅×#435	1	1	yes	characteristic
412	C₂	C₅×#2932	1	1	yes	characteristic
413	C₂	C₅×D₄×M₁₆	1	2	yes	—
414	C₂	C₅×#2935	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄×C₅	C₂⁴
commutator	C₂³	C₂³×C₄×C₅
Frattini, cosocle	C₂²×C₄	C₂⁴×C₅
socle	C₂³×C₅	C₂³×C₄
prime radical	C₂×C₅×#127	C₄
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₅×#436	C₂	semidirect
2. C₂×C₅×#435	C₂	semidirect
3. C₂×C₅×C₈×D₄	C₂	semidirect
5. C₅×#1955	C₂	semidirect
6. C₅×#1954	C₂	semidirect
7. C₅×#1954	C₂	semidirect
8. C₅×#1842	C₂	semidirect
9. C₄×C₅×#97	C₂	semidirect
35. #21682	C₅	direct (N × H)
77. C₅×#97	D₄	semidirect
79. C₄×C₅×C₈	D₄	semidirect
80. C₂×#436	C₂×C₅	semidirect
81. C₂×#435	C₂×C₅	semidirect
82. C₂×C₈×D₄	C₂×C₅	semidirect
84. #1955	C₂×C₅	semidirect
85. #1954	C₂×C₅	semidirect
86. #1954	C₂×C₅	semidirect
87. #1842	C₂×C₅	semidirect
88. C₄×#97	C₂×C₅	semidirect
99. C₂×C₅×D₄	M₁₆	semidirect
210. C₅×C₈	#127	semidirect
252. #97	C₅×D₄	semidirect
254. C₄×C₈	C₅×D₄	semidirect
275. C₄×C₅	#435	semidirect
289. C₂×D₄	C₅×M₁₆	semidirect
382. C₈	C₅×#127	semidirect
383. C₅	#21682	direct (N × H)
404. C₄	C₅×#435	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅×#436	2
C₂×C₅×#435	2
C₂×C₅×C₈×D₄	2
C₄×C₅×#127	2
C₅×#1955	2
C₅×#1954	2
C₅×#1842	2
C₄×C₅×#97	2
#21682	5

Subgroups — C5×#21682 #11944402

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#21682 #11944402