Subgroups — C₅×#17935 #11940655

Order 1280.

726 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#3100	C₂	1	1	yes	maximal, characteristic
2	C₅×#2931	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅×#436	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#1594	C₂	1	4	yes	maximal, complemented
5	C₅×#1586	C₂	1	4	yes	maximal, complemented
6	C₅×#1570	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#1486	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#1480	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#1452	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₅×#131	—	2	1	no	—
11	C₂²×C₅×M₁₆	—	2	1	no	—
12	C₅×#532	C₂²	1	1	yes	characteristic
13	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
14	C₅×#480	C₄	1	2	yes	—
15	C₅×#474	C₄	1	2	yes	—
16	C₅×#459	C₄	1	2	yes	—
17	C₅×#447	C₄	1	2	yes	—
18	C₄×C₅×D₈	C₂²	1	4	yes	—
19	C₅×#436	—	2	1	no	—
20	C₅×#436	—	2	1	no	—
21	C₅×#436	—	2	1	no	—
22	C₅×#436	C₂²	1	2	yes	—
23	C₅×#436	C₂²	1	2	yes	—
24	C₅×#436	C₂²	1	2	yes	complemented
25	C₅×C₈×D₄	—	2	1	no	—
26	C₅×C₈×D₄	C₂²	1	2	yes	complemented
27	C₅×#431	C₂²	1	1	yes	characteristic
28	C₅×#431	C₂²	1	1	yes	characteristic
29	C₅×#423	C₂²	1	1	yes	characteristic
30	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
31	C₅×#408	—	2	1	no	—
32	C₂×C₅×C₂²⋊C₈	—	2	1	no	—
33	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
34	C₅×#334	C₂²	1	4	yes	complemented
35	C₅×D₄⋊C₈	C₂²	1	4	yes	—
36	C₅×D₄⋊C₈	C₂²	1	4	yes	complemented
37	C₅×#322	C₂²	1	2	yes	complemented
38	C₅×#322	C₂²	1	2	yes	complemented
39	#17935	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
40	C₂×C₅×#41	—	2	1	no	—
41	C₂²×C₅×D₄	C₂×C₄	1	1	yes	characteristic
42	C₂³×C₄×C₅	—	2	1	no	—
43	C₂×C₅×D₈	C₂×C₄	1	4	yes	—
44	C₅×#131	—	4	4	no	—
45	C₂×C₅×M₁₆	—	2	1	no	—
46	C₂×C₅×M₁₆	—	2	2	no	—
47	C₂×C₅×M₁₆	—	2	2	no	—
48	C₂×C₅×M₁₆	—	2	2	no	—
49	C₂×C₅×M₁₆	—	4	4	no	—
50	C₂²×C₅×C₈	—	2	1	no	—
51	C₂²×C₅×C₈	—	2	2	no	—
52	C₂²×C₅×C₈	D₄	1	1	yes	characteristic
53	C₂²×C₅×C₈	D₄	1	1	yes	characteristic
54	C₅×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
55	C₅×#127	C₂×C₄	1	1	yes	characteristic
56	C₅×#124	—	2	1	no	—
57	C₅×#121	—	2	1	no	—
58	C₅×#121	C₂×C₄	1	2	yes	—
59	C₄×C₅×D₄	—	2	1	no	—
60	C₄×C₅×D₄	—	2	1	no	—
61	C₄×C₅×D₄	—	2	1	no	—
62	C₄×C₅×D₄	C₂×C₄	1	2	yes	—
63	C₄×C₅×D₄	C₂³	1	2	yes	—
64	C₄×C₅×D₄	C₂³	1	2	yes	—
65	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
66	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
67	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
68	C₅×#107	C₂×C₄	1	4	yes	—
69	C₅×C₄⋊C₈	—	2	1	no	—
70	C₅×C₄⋊C₈	—	2	1	no	—
71	C₅×C₄⋊C₈	—	2	1	no	—
72	C₅×C₄⋊C₈	C₂×C₄	1	2	yes	—
73	C₅×C₄⋊C₈	C₂³	1	2	yes	—
74	C₅×C₄⋊C₈	C₂³	1	2	yes	—
75	C₅×#102	C₂×C₄	1	4	yes	—
76	C₅×#102	C₂×C₄	1	4	yes	—
77	C₅×C₂²⋊C₈	—	2	1	no	—
78	C₅×C₂²⋊C₈	—	2	2	no	—
79	C₅×C₂²⋊C₈	—	2	2	no	—
80	C₅×C₂²⋊C₈	—	2	2	no	—
81	C₅×C₂²⋊C₈	—	2	2	no	—
82	C₅×C₂²⋊C₈	C₂×C₄	1	2	yes	—
83	C₄×C₅×C₈	D₄	1	1	yes	characteristic
84	C₄×C₅×C₈	D₄	1	1	yes	characteristic
85	C₄×C₅×C₈	C₂³	1	2	yes	—
86	C₄×C₅×C₈	C₂³	1	2	yes	—
87	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
88	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
89	#3100	C₂×C₅	1	1	yes	characteristic
90	#2931	C₂×C₅	1	1	yes	characteristic, complemented
91	C₂×#436	C₂×C₅	1	1	yes	characteristic, complemented
92	#1594	C₂×C₅	1	4	yes	complemented
93	#1586	C₂×C₅	1	4	yes	complemented
94	#1570	C₂×C₅	1	1	yes	characteristic, complemented
95	#1486	C₂×C₅	1	1	yes	characteristic, complemented
96	#1480	C₂×C₅	1	1	yes	characteristic, complemented
97	#1452	C₂×C₅	1	1	yes	characteristic, complemented
98	C₂⁴×C₅	—	2	1	no	—
99	C₅×#41	—	4	2	no	—
100	C₅×#41	—	4	2	no	—
101	C₂×C₅×Q₈	—	2	1	no	—
102	C₂×C₅×D₄	—	2	2	no	—
103	C₂×C₅×D₄	—	2	1	no	—
104	C₂×C₅×D₄	—	2	1	no	—
105	C₂×C₅×D₄	—	2	1	no	—
106	C₂×C₅×D₄	—	4	2	no	—
107	C₂×C₅×D₄	C₂²×C₄	1	2	yes	—
108	C₂×C₅×D₄	C₂²×C₄	1	2	yes	—
109	C₂²×C₄×C₅	—	2	1	no	—
110	C₂²×C₄×C₅	—	2	2	no	—
111	C₂²×C₄×C₅	—	2	2	no	—
112	C₂²×C₄×C₅	—	2	2	no	—
113	C₂²×C₄×C₅	—	4	2	no	—
114	C₂²×C₄×C₅	—	4	2	no	—
115	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
116	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
117	C₂²×C₄×C₅	#41	1	1	yes	characteristic
118	C₅×D₈	—	4	4	no	—
119	C₅×M₁₆	—	4	4	no	—
120	C₅×M₁₆	—	4	4	no	—
121	C₅×M₁₆	—	4	4	no	—
122	C₅×M₁₆	—	4	2	no	—
123	C₂×C₅×C₈	—	2	2	no	—
124	C₂×C₅×C₈	—	2	2	no	—
125	C₂×C₅×C₈	—	2	2	no	—
126	C₂×C₅×C₈	—	2	2	no	—
127	C₂×C₅×C₈	—	2	2	no	—
128	C₂×C₅×C₈	—	4	4	no	—
129	C₂×C₅×C₈	—	4	2	no	—
130	C₂×C₅×C₈	C₂²×C₄	1	4	yes	—
131	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
132	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
133	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
134	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
135	C₅×C₄⋊C₄	—	2	1	no	—
136	C₅×C₄⋊C₄	—	2	1	no	—
137	C₅×C₄⋊C₄	C₂²×C₄	1	2	yes	—
138	C₅×C₄⋊C₄	C₂²×C₄	1	2	yes	—
139	C₅×C₂²⋊C₄	—	2	2	no	—
140	C₅×C₂²⋊C₄	—	2	2	no	—
141	C₅×C₂²⋊C₄	—	2	2	no	—
142	C₅×C₂²⋊C₄	—	2	2	no	—
143	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
144	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
145	C₄²×C₅	#41	1	1	yes	characteristic
146	C₄²×C₅	C₂⁴	1	1	yes	characteristic
147	C₂×#131	—	2	1	no	—
148	C₂²×M₁₆	—	2	1	no	—
149	#532	C₂²×C₅	1	1	yes	characteristic
150	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
151	#480	C₄×C₅	1	2	yes	—
152	#474	C₄×C₅	1	2	yes	—
153	#459	C₄×C₅	1	2	yes	—
154	#447	C₄×C₅	1	2	yes	—
155	C₄×D₈	C₂²×C₅	1	4	yes	—
156	#436	—	2	1	no	—
157	#436	—	2	1	no	—
158	#436	—	2	1	no	—
159	#436	C₂²×C₅	1	2	yes	—
160	#436	C₂²×C₅	1	2	yes	—
161	#436	C₂²×C₅	1	2	yes	complemented
162	C₈×D₄	—	2	1	no	—
163	C₈×D₄	C₂²×C₅	1	2	yes	complemented
164	#431	C₂²×C₅	1	1	yes	characteristic
165	#431	C₂²×C₅	1	1	yes	characteristic
166	#423	C₂²×C₅	1	1	yes	characteristic
167	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
168	#408	—	2	1	no	—
169	C₂×C₂²⋊C₈	—	2	1	no	—
170	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
171	#334	C₂²×C₅	1	4	yes	complemented
172	D₄⋊C₈	C₂²×C₅	1	4	yes	—
173	D₄⋊C₈	C₂²×C₅	1	4	yes	complemented
174	#322	C₂²×C₅	1	2	yes	complemented
175	#322	C₂²×C₅	1	2	yes	complemented
176	C₂³×C₅	—	2	2	no	—
177	C₂³×C₅	—	2	2	no	—
178	C₂³×C₅	—	4	2	no	—
179	C₂³×C₅	—	4	2	no	—
180	C₂³×C₅	—	4	2	no	—
181	C₂³×C₅	C₄×D₄	1	1	yes	characteristic
182	C₅×Q₈	—	4	2	no	—
183	C₅×D₄	—	2	2	no	—
184	C₅×D₄	—	2	4	no	—
185	C₅×D₄	—	2	2	no	—
186	C₅×D₄	—	4	2	no	—
187	C₅×D₄	—	4	2	no	—
188	C₅×D₄	—	4	4	no	—
189	C₅×D₄	—	4	2	no	—
190	C₂×C₄×C₅	—	2	2	no	—
191	C₂×C₄×C₅	—	2	2	no	—
192	C₂×C₄×C₅	—	2	2	no	—
193	C₂×C₄×C₅	—	4	1	no	—
194	C₂×C₄×C₅	—	4	2	no	—
195	C₂×C₄×C₅	—	4	2	no	—
196	C₂×C₄×C₅	—	4	2	no	—
197	C₂×C₄×C₅	—	4	2	no	—
198	C₂×C₄×C₅	—	4	2	no	—
199	C₂×C₄×C₅	—	4	4	no	—
200	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
201	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
202	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
203	C₂×C₄×C₅	AGL(1,ℤ/8)	1	2	yes	—
204	C₂×C₄×C₅	AGL(1,ℤ/8)	1	2	yes	—
205	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
206	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
207	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
208	C₅×C₈	—	2	4	no	—
209	C₅×C₈	—	2	1	no	—
210	C₅×C₈	—	2	1	no	—
211	C₅×C₈	—	2	1	no	—
212	C₅×C₈	—	2	1	no	—
213	C₅×C₈	—	4	2	no	—
214	C₅×C₈	—	4	2	no	—
215	C₅×C₈	—	4	2	no	—
216	C₂×#41	—	2	1	no	—
217	C₂²×D₄	C₂×C₄×C₅	1	1	yes	characteristic
218	C₂³×C₄	—	2	1	no	—
219	C₂×D₈	C₂×C₄×C₅	1	4	yes	—
220	#131	—	4	4	no	—
221	C₂×M₁₆	—	2	1	no	—
222	C₂×M₁₆	—	2	2	no	—
223	C₂×M₁₆	—	2	2	no	—
224	C₂×M₁₆	—	2	2	no	—
225	C₂×M₁₆	—	4	4	no	—
226	C₂²×C₈	—	2	1	no	—
227	C₂²×C₈	—	2	2	no	—
228	C₂²×C₈	C₅×D₄	1	1	yes	characteristic
229	C₂²×C₈	C₅×D₄	1	1	yes	characteristic
230	C₄⋊Q₈	C₂×C₄×C₅	1	1	yes	characteristic
231	#127	C₂×C₄×C₅	1	1	yes	characteristic
232	#124	—	2	1	no	—
233	#121	—	2	1	no	—
234	#121	C₂×C₄×C₅	1	2	yes	—
235	C₄×D₄	—	2	1	no	—
236	C₄×D₄	—	2	1	no	—
237	C₄×D₄	—	2	1	no	—
238	C₄×D₄	C₂×C₄×C₅	1	2	yes	—
239	C₄×D₄	C₂³×C₅	1	2	yes	—
240	C₄×D₄	C₂³×C₅	1	2	yes	—
241	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
242	C₂×C₂²⋊C₄	—	2	1	no	—
243	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
244	#107	C₂×C₄×C₅	1	4	yes	—
245	C₄⋊C₈	—	2	1	no	—
246	C₄⋊C₈	—	2	1	no	—
247	C₄⋊C₈	—	2	1	no	—
248	C₄⋊C₈	C₂×C₄×C₅	1	2	yes	—
249	C₄⋊C₈	C₂³×C₅	1	2	yes	—
250	C₄⋊C₈	C₂³×C₅	1	2	yes	—
251	#102	C₂×C₄×C₅	1	4	yes	—
252	#102	C₂×C₄×C₅	1	4	yes	—
253	C₂²⋊C₈	—	2	1	no	—
254	C₂²⋊C₈	—	2	2	no	—
255	C₂²⋊C₈	—	2	2	no	—
256	C₂²⋊C₈	—	2	2	no	—
257	C₂²⋊C₈	—	2	2	no	—
258	C₂²⋊C₈	C₂×C₄×C₅	1	2	yes	—
259	C₄×C₈	C₅×D₄	1	1	yes	characteristic
260	C₄×C₈	C₅×D₄	1	1	yes	characteristic
261	C₄×C₈	C₂³×C₅	1	2	yes	—
262	C₄×C₈	C₂³×C₅	1	2	yes	—
263	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
264	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
265	C₂²×C₅	—	2	1	no	—
266	C₂²×C₅	—	2	1	no	—
267	C₂²×C₅	—	4	2	no	—
268	C₂²×C₅	—	4	2	no	—
269	C₂²×C₅	—	4	2	no	—
270	C₂²×C₅	—	4	2	no	—
271	C₂²×C₅	—	4	2	no	—
272	C₂²×C₅	—	4	2	no	—
273	C₂²×C₅	—	8	4	no	—
274	C₂²×C₅	#442	1	2	yes	—
275	C₂²×C₅	C₂×C₄×D₄	1	1	yes	characteristic
276	C₄×C₅	—	2	1	no	—
277	C₄×C₅	—	2	1	no	—
278	C₄×C₅	—	2	1	no	—
279	C₄×C₅	—	4	2	no	—
280	C₄×C₅	—	4	2	no	—
281	C₄×C₅	#442	1	2	yes	—
282	C₄×C₅	#568	1	2	yes	—
283	C₄×C₅	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
284	C₄×C₅	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
285	C₂⁴	—	2	1	no	—
286	#41	—	4	2	no	—
287	#41	—	4	2	no	—
288	C₂×Q₈	—	2	1	no	—
289	C₂×D₄	—	2	2	no	—
290	C₂×D₄	—	2	1	no	—
291	C₂×D₄	—	2	1	no	—
292	C₂×D₄	—	2	1	no	—
293	C₂×D₄	—	4	2	no	—
294	C₂×D₄	C₂²×C₄×C₅	1	2	yes	—
295	C₂×D₄	C₂²×C₄×C₅	1	2	yes	—
296	C₂²×C₄	—	2	1	no	—
297	C₂²×C₄	—	2	2	no	—
298	C₂²×C₄	—	2	2	no	—
299	C₂²×C₄	—	2	2	no	—
300	C₂²×C₄	—	4	2	no	—
301	C₂²×C₄	—	4	2	no	—
302	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
303	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
304	C₂²×C₄	C₅×#41	1	1	yes	characteristic
305	D₈	—	4	4	no	—
306	M₁₆	—	4	4	no	—
307	M₁₆	—	4	4	no	—
308	M₁₆	—	4	4	no	—
309	M₁₆	—	4	2	no	—
310	C₂×C₈	—	2	2	no	—
311	C₂×C₈	—	2	2	no	—
312	C₂×C₈	—	2	2	no	—
313	C₂×C₈	—	2	2	no	—
314	C₂×C₈	—	2	2	no	—
315	C₂×C₈	—	4	4	no	—
316	C₂×C₈	—	4	2	no	—
317	C₂×C₈	C₂²×C₄×C₅	1	4	yes	—
318	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
319	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
320	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
321	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
322	C₄⋊C₄	—	2	1	no	—
323	C₄⋊C₄	—	2	1	no	—
324	C₄⋊C₄	C₂²×C₄×C₅	1	2	yes	—
325	C₄⋊C₄	C₂²×C₄×C₅	1	2	yes	—
326	C₂²⋊C₄	—	2	2	no	—
327	C₂²⋊C₄	—	2	2	no	—
328	C₂²⋊C₄	—	2	2	no	—
329	C₂²⋊C₄	—	2	2	no	—
330	C₄²	C₂²×C₄×C₅	1	1	yes	characteristic
331	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
332	C₄²	C₅×#41	1	1	yes	characteristic
333	C₄²	C₂⁴×C₅	1	1	yes	characteristic
334	C₂×C₅	—	2	2	no	—
335	C₂×C₅	—	8	2	no	—
336	C₂×C₅	—	8	2	no	—
337	C₂×C₅	#2930	1	1	yes	characteristic
338	C₂×C₅	C₂×#442	1	1	yes	characteristic
339	C₂×C₅	#2955	1	1	yes	characteristic
340	C₂³	—	2	2	no	—
341	C₂³	—	2	2	no	—
342	C₂³	—	4	2	no	—
343	C₂³	—	4	2	no	—
344	C₂³	—	4	2	no	—
345	C₂³	C₄×C₅×D₄	1	1	yes	characteristic
346	Q₈	—	4	2	no	—
347	D₄	—	2	2	no	—
348	D₄	—	2	4	no	—
349	D₄	—	2	2	no	—
350	D₄	—	4	2	no	—
351	D₄	—	4	2	no	—
352	D₄	—	4	4	no	—
353	D₄	—	4	2	no	—
354	C₂×C₄	—	2	2	no	—
355	C₂×C₄	—	2	2	no	—
356	C₂×C₄	—	2	2	no	—
357	C₂×C₄	—	4	1	no	—
358	C₂×C₄	—	4	2	no	—
359	C₂×C₄	—	4	4	no	—
360	C₂×C₄	—	4	2	no	—
361	C₂×C₄	—	4	2	no	—
362	C₂×C₄	—	4	2	no	—
363	C₂×C₄	—	4	2	no	—
364	C₂×C₄	C₄×C₅×D₄	1	1	yes	characteristic
365	C₂×C₄	C₄×C₅×D₄	1	1	yes	characteristic
366	C₂×C₄	C₄×C₅×D₄	1	1	yes	characteristic
367	C₂×C₄	C₅×AGL(1,ℤ/8)	1	2	yes	—
368	C₂×C₄	C₅×AGL(1,ℤ/8)	1	2	yes	—
369	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
370	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
371	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
372	C₈	—	2	4	no	—
373	C₈	—	2	1	no	—
374	C₈	—	2	1	no	—
375	C₈	—	2	1	no	—
376	C₈	—	2	1	no	—
377	C₈	—	4	2	no	—
378	C₈	—	4	2	no	—
379	C₈	—	4	2	no	—
380	C₅	#17935	1	1	yes	characteristic, direct product factor, Sylow
381	C₂²	—	2	1	no	—
382	C₂²	—	2	1	no	—
383	C₂²	—	4	2	no	—
384	C₂²	—	4	2	no	—
385	C₂²	—	4	2	no	—
386	C₂²	—	4	2	no	—
387	C₂²	—	4	2	no	—
388	C₂²	—	4	2	no	—
389	C₂²	—	8	4	no	—
390	C₂²	C₅×#442	1	2	yes	—
391	C₂²	C₂×C₄×C₅×D₄	1	1	yes	characteristic
392	C₄	—	2	1	no	—
393	C₄	—	2	1	no	—
394	C₄	—	2	1	no	—
395	C₄	—	4	2	no	—
396	C₄	—	4	2	no	—
397	C₄	C₅×#442	1	2	yes	—
398	C₄	C₅×#568	1	2	yes	—
399	C₄	C₂×C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
400	C₄	C₂×C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
401	C₂	—	2	2	no	—
402	C₂	—	8	2	no	—
403	C₂	—	8	2	no	—
404	C₂	C₅×#2930	1	1	yes	characteristic
405	C₂	C₂×C₅×#442	1	1	yes	characteristic
406	C₂	C₅×#2955	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₅	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₅
Frattini, cosocle	C₄²	C₂⁴×C₅
socle	C₂²×C₅	C₂×C₄×D₄
prime radical	C₅×#3100	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₅ ◁ C₂×C₄×C₅×C₈ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₅×#2931	C₂	semidirect
3. C₂×C₅×#436	C₂	semidirect
4. C₅×#1594	C₂	semidirect
5. C₅×#1586	C₂	semidirect
6. C₅×#1570	C₂	semidirect
7. C₅×#1486	C₂	semidirect
8. C₅×#1480	C₂	semidirect
9. C₅×#1452	C₂	semidirect
24. C₅×#436	C₂²	semidirect
26. C₅×C₈×D₄	C₂²	semidirect
34. C₅×#334	C₂²	semidirect
36. C₅×D₄⋊C₈	C₂²	semidirect
37. C₅×#322	C₂²	semidirect
38. C₅×#322	C₂²	semidirect
39. #17935	C₅	direct (N × H)
90. #2931	C₂×C₅	semidirect
91. C₂×#436	C₂×C₅	semidirect
92. #1594	C₂×C₅	semidirect
93. #1586	C₂×C₅	semidirect
94. #1570	C₂×C₅	semidirect
95. #1486	C₂×C₅	semidirect
96. #1480	C₂×C₅	semidirect
97. #1452	C₂×C₅	semidirect
161. #436	C₂²×C₅	semidirect
163. C₈×D₄	C₂²×C₅	semidirect
171. #334	C₂²×C₅	semidirect
173. D₄⋊C₈	C₂²×C₅	semidirect
174. #322	C₂²×C₅	semidirect
175. #322	C₂²×C₅	semidirect
380. C₅	#17935	direct (N × H)

Maximal subgroups

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

subgroup	index
C₅×#3100	2
C₅×#2931	2
C₂×C₅×#436	2
C₅×#1594	2
C₅×#1586	2
C₅×#1570	2
C₅×#1486	2
C₅×#1480	2
C₅×#1452	2
#17935	5

Subgroups — C5×#17935 #11940655

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#17935 #11940655