Subgroups — C₅×#21693 #11944413

Order 1280.

1126 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#495	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅×#442	C₂	1	1	yes	maximal, characteristic
3	C₂×C₅×#441	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₅×#440	C₂	1	2	yes	maximal, complemented
5	C₄×C₅×#124	C₂	1	2	yes	maximal, complemented
6	C₅×#1973	C₂	1	2	yes	maximal, complemented
7	C₅×#1972	C₂	1	1	yes	maximal, characteristic
8	C₅×#1971	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#1958	C₂	1	2	yes	maximal, complemented
10	C₅×#1846	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×C₅×#97	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×C₅×Q₁₆	C₂²	1	1	yes	characteristic
13	C₂²×C₅×SD₁₆	C₂²	1	2	yes	—
14	C₂²×C₅×D₈	C₂²	1	1	yes	characteristic
15	C₂×C₅×#124	C₂²	1	2	yes	—
16	C₂×C₄×C₅×Q₈	C₂²	1	2	yes	—
17	C₂×C₄×C₅×D₄	C₂²	1	2	yes	—
18	C₅×#495	C₄	1	8	yes	complemented
19	C₅×#442	—	2	4	no	—
20	C₅×#441	—	2	4	no	—
21	C₅×#440	—	2	8	no	—
22	C₂×C₅×#107	C₂²	1	2	yes	—
23	C₂×C₅×#106	C₂²	1	1	yes	characteristic
24	C₂×C₅×#106	C₂²	1	1	yes	characteristic
25	C₂×C₅×#103	C₂²	1	2	yes	—
26	C₂×C₅×#103	C₂²	1	2	yes	—
27	C₂×C₅×#102	C₂²	1	2	yes	—
28	C₂×C₅×#102	C₂²	1	2	yes	—
29	C₂×C₅×#97	C₂²	1	1	yes	characteristic
30	C₂×C₅×#97	C₂²	1	1	yes	characteristic
31	C₂×C₅×#97	C₂²	1	1	yes	characteristic
32	C₂×C₅×#97	C₂²	1	1	yes	characteristic
33	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
34	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
35	C₅×#391	C₂²	1	2	yes	—
36	C₅×#390	C₂²	1	2	yes	—
37	C₅×#388	—	2	4	no	—
38	C₅×#382	C₂²	1	2	yes	—
39	C₄×C₅×C₂²⋊C₄	—	2	4	no	—
40	C₄³×C₅	C₂²	1	1	yes	characteristic
41	#21693	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
42	C₂²×C₅×Q₈	C₂³	1	2	yes	—
43	C₂²×C₅×D₄	C₂³	1	2	yes	—
44	C₂³×C₄×C₅	—	2	2	no	—
45	C₂×C₅×Q₁₆	—	2	2	no	—
46	C₂×C₅×Q₁₆	—	2	2	no	—
47	C₂×C₅×Q₁₆	C₂×C₄	1	4	yes	complemented
48	C₂×C₅×SD₁₆	—	2	4	no	—
49	C₂×C₅×SD₁₆	—	2	4	no	—
50	C₂×C₅×SD₁₆	C₂×C₄	1	8	yes	complemented
51	C₂×C₅×D₈	—	2	2	no	—
52	C₂×C₅×D₈	—	2	2	no	—
53	C₂×C₅×D₈	C₂×C₄	1	4	yes	—
54	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
55	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
56	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
57	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
58	C₅×#124	—	2	4	no	—
59	C₅×#124	C₂×C₄	1	8	yes	complemented
60	C₄×C₅×Q₈	—	2	4	no	—
61	C₄×C₅×Q₈	—	2	4	no	—
62	C₄×C₅×D₄	—	2	4	no	—
63	C₄×C₅×D₄	—	2	4	no	—
64	C₂×C₅×C₄⋊C₄	—	2	2	no	—
65	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
66	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
67	C₂×C₅×C₂²⋊C₄	—	2	4	no	—
68	C₂×C₅×C₂²⋊C₄	—	2	4	no	—
69	C₂×C₅×C₂²⋊C₄	—	2	2	no	—
70	C₂×C₄²×C₅	—	2	2	no	—
71	C₂×C₄²×C₅	D₄	1	4	yes	—
72	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
73	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
74	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
75	C₅×#107	—	2	4	no	—
76	C₅×#106	—	2	2	no	—
77	C₅×#106	—	2	2	no	—
78	C₅×#103	—	2	4	no	—
79	C₅×#103	—	2	4	no	—
80	C₅×#102	—	2	4	no	—
81	C₅×#102	—	2	4	no	—
82	C₅×#97	—	2	2	no	—
83	C₅×#97	—	2	2	no	—
84	C₅×#97	D₄	1	4	yes	—
85	C₅×#97	D₄	1	4	yes	—
86	C₄×C₅×C₈	—	2	2	no	—
87	C₄×C₅×C₈	C₂×C₄	1	4	yes	complemented
88	C₅×#95	—	2	4	no	—
89	C₅×#95	—	2	4	no	—
90	C₂×#495	C₂×C₅	1	1	yes	characteristic
91	C₂×#442	C₂×C₅	1	1	yes	characteristic
92	C₂×#441	C₂×C₅	1	1	yes	characteristic, complemented
93	C₂×#440	C₂×C₅	1	2	yes	complemented
94	C₄×#124	C₂×C₅	1	2	yes	complemented
95	#1973	C₂×C₅	1	2	yes	complemented
96	#1972	C₂×C₅	1	1	yes	characteristic
97	#1971	C₂×C₅	1	1	yes	characteristic, complemented
98	#1958	C₂×C₅	1	2	yes	complemented
99	#1846	C₂×C₅	1	1	yes	characteristic, complemented
100	C₄×#97	C₂×C₅	1	1	yes	characteristic, complemented
101	C₂⁴×C₅	—	2	2	no	—
102	C₂×C₅×Q₈	—	2	2	no	—
103	C₂×C₅×Q₈	—	2	2	no	—
104	C₂×C₅×Q₈	—	2	2	no	—
105	C₂×C₅×Q₈	—	2	2	no	—
106	C₂×C₅×Q₈	—	2	2	no	—
107	C₂×C₅×Q₈	C₂²×C₄	1	4	yes	—
108	C₂×C₅×D₄	—	2	2	no	—
109	C₂×C₅×D₄	—	2	2	no	—
110	C₂×C₅×D₄	—	2	2	no	—
111	C₂×C₅×D₄	—	2	2	no	—
112	C₂×C₅×D₄	—	2	2	no	—
113	C₂×C₅×D₄	C₂²×C₄	1	4	yes	—
114	C₂²×C₄×C₅	—	2	2	no	—
115	C₂²×C₄×C₅	—	2	2	no	—
116	C₂²×C₄×C₅	—	2	2	no	—
117	C₂²×C₄×C₅	—	4	8	no	—
118	C₂²×C₄×C₅	—	4	4	no	—
119	C₂²×C₄×C₅	C₂×D₄	1	2	yes	—
120	C₂²×C₄×C₅	C₂×D₄	1	2	yes	—
121	C₂²×C₄×C₅	C₂×D₄	1	2	yes	—
122	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
123	C₅×Q₁₆	—	2	8	no	—
124	C₅×SD₁₆	—	2	16	no	—
125	C₅×D₈	—	2	8	no	—
126	C₂×C₅×C₈	—	2	1	no	—
127	C₂×C₅×C₈	—	2	1	no	—
128	C₂×C₅×C₈	—	2	1	no	—
129	C₂×C₅×C₈	—	2	1	no	—
130	C₂×C₅×C₈	C₂²×C₄	1	2	yes	—
131	C₂×C₅×C₈	C₂²×C₄	1	2	yes	—
132	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
133	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
134	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
135	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
136	C₂×C₅×C₈	#41	1	2	yes	—
137	C₂×C₅×C₈	#41	1	2	yes	—
138	C₅×C₄⋊C₄	—	2	2	no	—
139	C₅×C₄⋊C₄	—	2	2	no	—
140	C₅×C₄⋊C₄	—	2	2	no	—
141	C₅×C₄⋊C₄	—	2	2	no	—
142	C₅×C₄⋊C₄	—	4	4	no	—
143	C₅×C₂²⋊C₄	—	2	16	no	—
144	C₅×C₂²⋊C₄	—	4	8	no	—
145	C₅×C₂²⋊C₄	—	4	4	no	—
146	C₄²×C₅	—	2	1	no	—
147	C₄²×C₅	—	2	1	no	—
148	C₄²×C₅	—	4	4	no	—
149	C₄²×C₅	—	4	4	no	—
150	C₄²×C₅	C₂²×C₄	1	2	yes	—
151	C₄²×C₅	C₂×D₄	1	2	yes	—
152	C₄²×C₅	C₂×D₄	1	2	yes	—
153	C₄²×C₅	#41	1	2	yes	—
154	C₂²×Q₁₆	C₂²×C₅	1	1	yes	characteristic
155	C₂²×SD₁₆	C₂²×C₅	1	2	yes	—
156	C₂²×D₈	C₂²×C₅	1	1	yes	characteristic
157	C₂×#124	C₂²×C₅	1	2	yes	—
158	C₂×C₄×Q₈	C₂²×C₅	1	2	yes	—
159	C₂×C₄×D₄	C₂²×C₅	1	2	yes	—
160	#495	C₄×C₅	1	8	yes	complemented
161	#442	—	2	4	no	—
162	#441	—	2	4	no	—
163	#440	—	2	8	no	—
164	C₂×#107	C₂²×C₅	1	2	yes	—
165	C₂×#106	C₂²×C₅	1	1	yes	characteristic
166	C₂×#106	C₂²×C₅	1	1	yes	characteristic
167	C₂×#103	C₂²×C₅	1	2	yes	—
168	C₂×#103	C₂²×C₅	1	2	yes	—
169	C₂×#102	C₂²×C₅	1	2	yes	—
170	C₂×#102	C₂²×C₅	1	2	yes	—
171	C₂×#97	C₂²×C₅	1	1	yes	characteristic
172	C₂×#97	C₂²×C₅	1	1	yes	characteristic
173	C₂×#97	C₂²×C₅	1	1	yes	characteristic
174	C₂×#97	C₂²×C₅	1	1	yes	characteristic
175	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
176	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
177	#391	C₂²×C₅	1	2	yes	—
178	#390	C₂²×C₅	1	2	yes	—
179	#388	—	2	4	no	—
180	#382	C₂²×C₅	1	2	yes	—
181	C₄×C₂²⋊C₄	—	2	4	no	—
182	C₄³	C₂²×C₅	1	1	yes	characteristic
183	C₂³×C₅	—	2	4	no	—
184	C₂³×C₅	—	4	2	no	—
185	C₂³×C₅	—	4	2	no	—
186	C₂³×C₅	—	4	4	no	—
187	C₂³×C₅	—	4	4	no	—
188	C₂³×C₅	C₂²×D₄	1	1	yes	characteristic
189	C₅×Q₈	—	2	4	no	—
190	C₅×Q₈	—	2	4	no	—
191	C₅×Q₈	—	4	2	no	—
192	C₅×Q₈	—	4	2	no	—
193	C₅×D₄	—	2	4	no	—
194	C₅×D₄	—	2	4	no	—
195	C₅×D₄	—	4	2	no	—
196	C₅×D₄	—	4	2	no	—
197	C₂×C₄×C₅	—	2	4	no	—
198	C₂×C₄×C₅	—	2	4	no	—
199	C₂×C₄×C₅	—	2	4	no	—
200	C₂×C₄×C₅	—	2	2	no	—
201	C₂×C₄×C₅	—	2	4	no	—
202	C₂×C₄×C₅	—	4	2	no	—
203	C₂×C₄×C₅	—	4	2	no	—
204	C₂×C₄×C₅	—	4	2	no	—
205	C₂×C₄×C₅	—	4	2	no	—
206	C₂×C₄×C₅	—	4	4	no	—
207	C₂×C₄×C₅	—	4	4	no	—
208	C₂×C₄×C₅	—	8	8	no	—
209	C₂×C₄×C₅	C₄×D₄	1	4	yes	—
210	C₂×C₄×C₅	#127	1	4	yes	—
211	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
212	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
213	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
214	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
215	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
216	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
217	C₅×C₈	—	2	2	no	—
218	C₅×C₈	—	2	2	no	—
219	C₅×C₈	C₄×D₄	1	4	yes	—
220	C₅×C₈	C₄×D₄	1	4	yes	—
221	C₂²×Q₈	C₂³×C₅	1	2	yes	—
222	C₂²×D₄	C₂³×C₅	1	2	yes	—
223	C₂³×C₄	—	2	2	no	—
224	C₂×Q₁₆	—	2	2	no	—
225	C₂×Q₁₆	—	2	2	no	—
226	C₂×Q₁₆	C₂×C₄×C₅	1	4	yes	complemented
227	C₂×SD₁₆	—	2	4	no	—
228	C₂×SD₁₆	—	2	4	no	—
229	C₂×SD₁₆	C₂×C₄×C₅	1	8	yes	complemented
230	C₂×D₈	—	2	2	no	—
231	C₂×D₈	—	2	2	no	—
232	C₂×D₈	C₂×C₄×C₅	1	4	yes	—
233	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
234	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
235	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
236	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
237	#124	—	2	4	no	—
238	#124	C₂×C₄×C₅	1	8	yes	complemented
239	C₄×Q₈	—	2	4	no	—
240	C₄×Q₈	—	2	4	no	—
241	C₄×D₄	—	2	4	no	—
242	C₄×D₄	—	2	4	no	—
243	C₂×C₄⋊C₄	—	2	2	no	—
244	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
245	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
246	C₂×C₂²⋊C₄	—	2	4	no	—
247	C₂×C₂²⋊C₄	—	2	2	no	—
248	C₂×C₂²⋊C₄	—	2	4	no	—
249	C₂×C₄²	—	2	2	no	—
250	C₂×C₄²	C₅×D₄	1	4	yes	—
251	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
252	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
253	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
254	#107	—	2	4	no	—
255	#106	—	2	2	no	—
256	#106	—	2	2	no	—
257	#103	—	2	4	no	—
258	#103	—	2	4	no	—
259	#102	—	2	4	no	—
260	#102	—	2	4	no	—
261	#97	—	2	2	no	—
262	#97	—	2	2	no	—
263	#97	C₅×D₄	1	4	yes	—
264	#97	C₅×D₄	1	4	yes	—
265	C₄×C₈	—	2	2	no	—
266	C₄×C₈	C₂×C₄×C₅	1	4	yes	complemented
267	#95	—	2	4	no	—
268	#95	—	2	4	no	—
269	C₂²×C₅	—	4	4	no	—
270	C₂²×C₅	—	4	8	no	—
271	C₂²×C₅	—	8	2	no	—
272	C₂²×C₅	—	8	2	no	—
273	C₂²×C₅	—	8	4	no	—
274	C₂²×C₅	C₂×C₄×D₄	1	1	yes	characteristic
275	C₂²×C₅	C₂×#127	1	1	yes	characteristic
276	C₂²×C₅	#532	1	1	yes	characteristic
277	C₂²×C₅	#575	1	4	yes	—
278	C₄×C₅	—	2	4	no	—
279	C₄×C₅	—	2	4	no	—
280	C₄×C₅	—	4	4	no	—
281	C₄×C₅	—	4	2	no	—
282	C₄×C₅	—	8	2	no	—
283	C₄×C₅	—	8	2	no	—
284	C₄×C₅	C₂×C₄×D₄	1	1	yes	characteristic
285	C₄×C₅	C₂×C₄×D₄	1	1	yes	characteristic
286	C₄×C₅	#532	1	1	yes	characteristic
287	C₄×C₅	#532	1	1	yes	characteristic
288	C₂⁴	—	2	2	no	—
289	C₂×Q₈	—	2	2	no	—
290	C₂×Q₈	—	2	2	no	—
291	C₂×Q₈	—	2	2	no	—
292	C₂×Q₈	—	2	2	no	—
293	C₂×Q₈	—	2	2	no	—
294	C₂×Q₈	C₂²×C₄×C₅	1	4	yes	—
295	C₂×D₄	—	2	2	no	—
296	C₂×D₄	—	2	2	no	—
297	C₂×D₄	—	2	2	no	—
298	C₂×D₄	—	2	2	no	—
299	C₂×D₄	—	2	2	no	—
300	C₂×D₄	C₂²×C₄×C₅	1	4	yes	—
301	C₂²×C₄	—	2	2	no	—
302	C₂²×C₄	—	2	2	no	—
303	C₂²×C₄	—	2	2	no	—
304	C₂²×C₄	—	4	8	no	—
305	C₂²×C₄	—	4	4	no	—
306	C₂²×C₄	C₂×C₅×D₄	1	2	yes	—
307	C₂²×C₄	C₂×C₅×D₄	1	2	yes	—
308	C₂²×C₄	C₂×C₅×D₄	1	2	yes	—
309	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
310	Q₁₆	—	2	8	no	—
311	SD₁₆	—	2	16	no	—
312	D₈	—	2	8	no	—
313	C₂×C₈	—	2	1	no	—
314	C₂×C₈	—	2	1	no	—
315	C₂×C₈	—	2	1	no	—
316	C₂×C₈	—	2	1	no	—
317	C₂×C₈	C₂²×C₄×C₅	1	2	yes	—
318	C₂×C₈	C₂²×C₄×C₅	1	2	yes	—
319	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
320	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
321	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
322	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
323	C₂×C₈	C₅×#41	1	2	yes	—
324	C₂×C₈	C₅×#41	1	2	yes	—
325	C₄⋊C₄	—	2	2	no	—
326	C₄⋊C₄	—	2	2	no	—
327	C₄⋊C₄	—	2	2	no	—
328	C₄⋊C₄	—	2	2	no	—
329	C₄⋊C₄	—	4	4	no	—
330	C₂²⋊C₄	—	2	16	no	—
331	C₂²⋊C₄	—	4	8	no	—
332	C₂²⋊C₄	—	4	4	no	—
333	C₄²	—	2	1	no	—
334	C₄²	—	2	1	no	—
335	C₄²	—	4	4	no	—
336	C₄²	—	4	4	no	—
337	C₄²	C₂²×C₄×C₅	1	2	yes	—
338	C₄²	C₂×C₅×D₄	1	2	yes	—
339	C₄²	C₂×C₅×D₄	1	2	yes	—
340	C₄²	C₅×#41	1	2	yes	—
341	C₂×C₅	—	8	4	no	—
342	C₂×C₅	C₄×#127	1	1	yes	characteristic
343	C₂×C₅	#2943	1	2	yes	—
344	C₂×C₅	#3153	1	2	yes	—
345	C₂×C₅	#3183	1	2	yes	—
346	C₂³	—	2	4	no	—
347	C₂³	—	4	2	no	—
348	C₂³	—	4	2	no	—
349	C₂³	—	4	4	no	—
350	C₂³	—	4	4	no	—
351	C₂³	C₂²×C₅×D₄	1	1	yes	characteristic
352	Q₈	—	2	4	no	—
353	Q₈	—	2	4	no	—
354	Q₈	—	4	2	no	—
355	Q₈	—	4	2	no	—
356	D₄	—	2	4	no	—
357	D₄	—	2	4	no	—
358	D₄	—	4	2	no	—
359	D₄	—	4	2	no	—
360	C₂×C₄	—	2	4	no	—
361	C₂×C₄	—	2	4	no	—
362	C₂×C₄	—	2	4	no	—
363	C₂×C₄	—	2	2	no	—
364	C₂×C₄	—	2	4	no	—
365	C₂×C₄	—	4	2	no	—
366	C₂×C₄	—	4	2	no	—
367	C₂×C₄	—	4	2	no	—
368	C₂×C₄	—	4	2	no	—
369	C₂×C₄	—	4	4	no	—
370	C₂×C₄	—	4	4	no	—
371	C₂×C₄	—	8	8	no	—
372	C₂×C₄	C₄×C₅×D₄	1	4	yes	—
373	C₂×C₄	C₅×#127	1	4	yes	—
374	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
375	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
376	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
377	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
378	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
379	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
380	C₈	—	2	2	no	—
381	C₈	—	2	2	no	—
382	C₈	C₄×C₅×D₄	1	4	yes	—
383	C₈	C₄×C₅×D₄	1	4	yes	—
384	C₅	#21693	1	1	yes	characteristic, direct product factor, Sylow
385	C₂²	—	4	4	no	—
386	C₂²	—	4	8	no	—
387	C₂²	—	8	2	no	—
388	C₂²	—	8	2	no	—
389	C₂²	—	8	4	no	—
390	C₂²	C₂×C₄×C₅×D₄	1	1	yes	characteristic
391	C₂²	C₂×C₅×#127	1	1	yes	characteristic
392	C₂²	C₅×#532	1	1	yes	characteristic
393	C₂²	C₅×#575	1	4	yes	—
394	C₄	—	2	4	no	—
395	C₄	—	2	4	no	—
396	C₄	—	4	4	no	—
397	C₄	—	4	2	no	—
398	C₄	—	8	2	no	—
399	C₄	—	8	2	no	—
400	C₄	C₂×C₄×C₅×D₄	1	1	yes	characteristic
401	C₄	C₂×C₄×C₅×D₄	1	1	yes	characteristic
402	C₄	C₅×#532	1	1	yes	characteristic
403	C₄	C₅×#532	1	1	yes	characteristic
404	C₂	—	8	4	no	—
405	C₂	C₄×C₅×#127	1	1	yes	characteristic
406	C₂	C₅×#2943	1	2	yes	—
407	C₂	C₅×#3153	1	2	yes	—
408	C₂	C₅×#3183	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₅	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₅
Frattini, cosocle	C₂²×C₄	C₂⁴×C₅
prime radical	C₂²×C₅×D₈	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₅ ◁ C₄³×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₂×C₅×#441	C₂	semidirect
4. C₂×C₅×#440	C₂	semidirect
5. C₄×C₅×#124	C₂	semidirect
6. C₅×#1973	C₂	semidirect
8. C₅×#1971	C₂	semidirect
9. C₅×#1958	C₂	semidirect
10. C₅×#1846	C₂	semidirect
11. C₄×C₅×#97	C₂	semidirect
18. C₅×#495	C₄	semidirect
41. #21693	C₅	direct (N × H)
47. C₂×C₅×Q₁₆	C₂×C₄	semidirect
50. C₂×C₅×SD₁₆	C₂×C₄	semidirect
59. C₅×#124	C₂×C₄	semidirect
87. C₄×C₅×C₈	C₂×C₄	semidirect
92. C₂×#441	C₂×C₅	semidirect
93. C₂×#440	C₂×C₅	semidirect
94. C₄×#124	C₂×C₅	semidirect
95. #1973	C₂×C₅	semidirect
97. #1971	C₂×C₅	semidirect
98. #1958	C₂×C₅	semidirect
99. #1846	C₂×C₅	semidirect
100. C₄×#97	C₂×C₅	semidirect
160. #495	C₄×C₅	semidirect
226. C₂×Q₁₆	C₂×C₄×C₅	semidirect
229. C₂×SD₁₆	C₂×C₄×C₅	semidirect
238. #124	C₂×C₄×C₅	semidirect
266. C₄×C₈	C₂×C₄×C₅	semidirect
384. C₅	#21693	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×#495	2
C₂×C₅×#442	2
C₂×C₅×#441	2
C₂×C₅×#440	2
C₄×C₅×#124	2
C₅×#1973	2
C₅×#1972	2
C₅×#1971	2
C₅×#1958	2
C₅×#1846	2
C₄×C₅×#97	2
#21693	5

Subgroups — C5×#21693 #11944413

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#21693 #11944413