Subgroups — C₅×#22290 #11945010

Order 1280.

702 conjugacy classes of subgroups.

The subgroup lattice has 414 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#2396	C₂	1	1	yes	maximal, characteristic
2	C₅×#1984	C₂	1	2	yes	maximal, complemented
3	C₅×#1940	C₂	1	2	yes	maximal, complemented
4	C₅×#1917	C₂	1	2	yes	maximal, complemented
5	C₅×#1916	C₂	1	2	yes	maximal, complemented
6	C₅×#1850	C₂	1	2	yes	maximal
7	C₅×#1798	C₂	1	1	yes	maximal, characteristic
8	C₅×#1753	C₂	1	2	yes	maximal
9	C₅×#1729	C₂	1	1	yes	maximal, characteristic
10	C₂²×C₅×M₁₆	C₂²	1	1	yes	characteristic
11	C₂³×C₅×C₈	C₂²	1	1	yes	characteristic
12	C₂×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
13	C₂×C₅×#117	C₂²	1	1	yes	characteristic
14	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
15	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
16	C₂×C₅×C₄⋊C₈	C₂²	1	2	yes	—
17	C₂×C₅×C₄⋊C₈	C₂²	1	2	yes	—
18	C₂×C₅×C₂²⋊C₈	C₂²	1	2	yes	—
19	C₂×C₅×#97	C₂²	1	2	yes	—
20	C₂×C₄×C₅×C₈	C₂²	1	2	yes	—
21	C₅×#400	C₄	1	1	yes	characteristic
22	C₅×#399	C₄	1	1	yes	characteristic
23	C₅×#398	C₄	1	2	yes	—
24	C₅×#396	C₄	1	2	yes	—
25	C₅×#395	C₄	1	1	yes	characteristic
26	C₅×#393	C₄	1	1	yes	characteristic
27	C₄×C₅×C₄⋊C₄	C₂²	1	2	yes	—
28	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
29	C₄×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
30	C₅×#336	C₂²	1	2	yes	—
31	C₅×#336	C₂²	1	2	yes	—
32	C₅×#336	C₂²	1	2	yes	—
33	C₅×#336	C₂²	1	2	yes	—
34	C₅×#336	C₂²	1	2	yes	—
35	C₅×#336	C₂²	1	2	yes	—
36	C₅×#336	C₂²	1	2	yes	—
37	#22290	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
38	C₂²×C₅×Q₈	C₂×C₄	1	1	yes	characteristic
39	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
40	C₂×C₅×M₁₆	—	4	1	no	—
41	C₂×C₅×M₁₆	—	4	1	no	—
42	C₂×C₅×M₁₆	Q₈	1	4	yes	complemented
43	C₂²×C₅×C₈	—	2	2	no	—
44	C₂²×C₅×C₈	—	4	1	no	—
45	C₂²×C₅×C₈	—	4	1	no	—
46	C₂²×C₅×C₈	C₂³	1	2	yes	—
47	C₂²×C₅×C₈	C₂³	1	2	yes	—
48	C₂²×C₅×C₈	C₂³	1	2	yes	—
49	C₂²×C₅×C₈	C₂³	1	2	yes	—
50	C₄×C₅×Q₈	—	4	1	no	—
51	C₄×C₅×Q₈	—	4	1	no	—
52	C₅×#117	—	4	1	no	—
53	C₅×#117	—	4	1	no	—
54	C₂×C₅×C₄⋊C₄	C₂×C₄	1	2	yes	—
55	C₂×C₅×C₄⋊C₄	C₂×C₄	1	2	yes	—
56	C₂×C₅×C₄⋊C₄	C₂×C₄	1	2	yes	—
57	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
58	C₂×C₅×C₄⋊C₄	C₂×C₄	1	2	yes	—
59	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
60	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
61	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	2	yes	—
62	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	2	yes	—
63	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
64	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
65	C₂×C₄²×C₅	C₂³	1	2	yes	—
66	C₂×C₄²×C₅	C₂³	1	2	yes	—
67	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
68	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
69	C₅×C₄⋊C₈	—	4	1	no	—
70	C₅×C₄⋊C₈	—	4	1	no	—
71	C₅×C₄⋊C₈	—	4	2	no	—
72	C₅×C₄⋊C₈	—	4	2	no	—
73	C₅×C₂²⋊C₈	—	2	4	no	—
74	C₅×#97	—	4	2	no	—
75	C₄×C₅×C₈	—	4	2	no	—
76	C₅×#95	C₂×C₄	1	2	yes	—
77	C₅×#95	C₂×C₄	1	2	yes	—
78	C₅×#95	C₂×C₄	1	2	yes	—
79	C₅×#95	C₂×C₄	1	1	yes	characteristic
80	C₅×#95	C₂×C₄	1	1	yes	characteristic
81	C₅×#95	C₂×C₄	1	2	yes	—
82	#2396	C₂×C₅	1	1	yes	characteristic
83	#1984	C₂×C₅	1	2	yes	complemented
84	#1940	C₂×C₅	1	2	yes	complemented
85	#1917	C₂×C₅	1	2	yes	complemented
86	#1916	C₂×C₅	1	2	yes	complemented
87	#1850	C₂×C₅	1	2	yes	—
88	#1798	C₂×C₅	1	1	yes	characteristic
89	#1753	C₂×C₅	1	2	yes	—
90	#1729	C₂×C₅	1	1	yes	characteristic
91	C₂⁴×C₅	C₂²×C₄	1	1	yes	characteristic
92	C₂×C₅×Q₈	—	2	4	no	—
93	C₂×C₅×Q₈	—	4	1	no	—
94	C₂²×C₄×C₅	—	2	1	no	—
95	C₂²×C₄×C₅	—	2	1	no	—
96	C₂²×C₄×C₅	—	2	1	no	—
97	C₂²×C₄×C₅	—	2	1	no	—
98	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
99	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
100	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
101	C₂²×C₄×C₅	C₂²×C₄	1	2	yes	—
102	C₂²×C₄×C₅	C₂²×C₄	1	2	yes	—
103	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
104	C₂²×C₄×C₅	C₂²×C₄	1	2	yes	—
105	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
106	C₂²×C₄×C₅	C₂²×C₄	1	2	yes	—
107	C₂²×C₄×C₅	C₂×Q₈	1	2	yes	—
108	C₂²×C₄×C₅	#41	1	2	yes	—
109	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
110	C₅×M₁₆	—	4	4	no	—
111	C₂×C₅×C₈	—	2	2	no	—
112	C₂×C₅×C₈	—	2	2	no	—
113	C₂×C₅×C₈	—	2	2	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	—	2	2	no	—
122	C₂×C₅×C₈	—	4	4	no	—
123	C₂×C₅×C₈	C₂×Q₈	1	4	yes	—
124	C₅×C₄⋊C₄	—	2	4	no	—
125	C₅×C₄⋊C₄	—	4	2	no	—
126	C₅×C₄⋊C₄	—	4	2	no	—
127	C₅×C₄⋊C₄	—	4	1	no	—
128	C₅×C₄⋊C₄	—	4	1	no	—
129	C₅×C₄⋊C₄	—	4	2	no	—
130	C₅×C₄⋊C₄	—	4	1	no	—
131	C₅×C₂²⋊C₄	—	2	4	no	—
132	C₅×C₂²⋊C₄	—	4	2	no	—
133	C₅×C₂²⋊C₄	—	4	1	no	—
134	C₅×C₂²⋊C₄	—	4	1	no	—
135	C₄²×C₅	—	2	1	no	—
136	C₄²×C₅	—	2	1	no	—
137	C₄²×C₅	—	2	1	no	—
138	C₄²×C₅	—	2	1	no	—
139	C₄²×C₅	—	2	2	no	—
140	C₄²×C₅	—	2	2	no	—
141	C₄²×C₅	—	2	2	no	—
142	C₄²×C₅	—	2	2	no	—
143	C₂²×M₁₆	C₂²×C₅	1	1	yes	characteristic
144	C₂³×C₈	C₂²×C₅	1	1	yes	characteristic
145	C₂×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
146	C₂×#117	C₂²×C₅	1	1	yes	characteristic
147	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
148	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
149	C₂×C₄⋊C₈	C₂²×C₅	1	2	yes	—
150	C₂×C₄⋊C₈	C₂²×C₅	1	2	yes	—
151	C₂×C₂²⋊C₈	C₂²×C₅	1	2	yes	—
152	C₂×#97	C₂²×C₅	1	2	yes	—
153	C₂×C₄×C₈	C₂²×C₅	1	2	yes	—
154	#400	C₄×C₅	1	1	yes	characteristic
155	#399	C₄×C₅	1	1	yes	characteristic
156	#398	C₄×C₅	1	2	yes	—
157	#396	C₄×C₅	1	2	yes	—
158	#395	C₄×C₅	1	1	yes	characteristic
159	#393	C₄×C₅	1	1	yes	characteristic
160	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	—
161	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
162	C₄×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
163	#336	C₂²×C₅	1	2	yes	—
164	#336	C₂²×C₅	1	2	yes	—
165	#336	C₂²×C₅	1	2	yes	—
166	#336	C₂²×C₅	1	2	yes	—
167	#336	C₂²×C₅	1	2	yes	—
168	#336	C₂²×C₅	1	2	yes	—
169	#336	C₂²×C₅	1	2	yes	—
170	C₂³×C₅	—	2	1	no	—
171	C₂³×C₅	—	2	1	no	—
172	C₂³×C₅	—	2	2	no	—
173	C₂³×C₅	—	2	2	no	—
174	C₂³×C₅	C₄×Q₈	1	2	yes	—
175	C₂³×C₅	C₂³×C₄	1	1	yes	characteristic
176	C₅×Q₈	—	4	4	no	—
177	C₂×C₄×C₅	—	2	2	no	—
178	C₂×C₄×C₅	—	2	1	no	—
179	C₂×C₄×C₅	—	2	1	no	—
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	—	2	2	no	—
184	C₂×C₄×C₅	—	2	2	no	—
185	C₂×C₄×C₅	—	2	1	no	—
186	C₂×C₄×C₅	—	2	1	no	—
187	C₂×C₄×C₅	—	2	1	no	—
188	C₂×C₄×C₅	—	2	1	no	—
189	C₂×C₄×C₅	—	2	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	—	2	2	no	—
194	C₂×C₄×C₅	—	2	2	no	—
195	C₂×C₄×C₅	—	2	2	no	—
196	C₂×C₄×C₅	—	2	2	no	—
197	C₂×C₄×C₅	—	2	2	no	—
198	C₂×C₄×C₅	—	2	2	no	—
199	C₂×C₄×C₅	—	2	2	no	—
200	C₂×C₄×C₅	—	2	2	no	—
201	C₂×C₄×C₅	—	2	2	no	—
202	C₂×C₄×C₅	C₄×Q₈	1	2	yes	—
203	C₂×C₄×C₅	#131	1	4	yes	—
204	C₂×C₄×C₅	C₂²×Q₈	1	1	yes	characteristic
205	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
206	C₂×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
207	C₂×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
208	C₂×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
209	C₂×C₄×C₅	2₋¹⁺⁴	1	1	yes	characteristic
210	C₅×C₈	—	2	4	no	—
211	C₅×C₈	—	4	2	no	—
212	C₅×C₈	—	4	2	no	—
213	C₅×C₈	—	4	2	no	—
214	C₂²×Q₈	C₂×C₄×C₅	1	1	yes	characteristic
215	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
216	C₂×M₁₆	—	4	1	no	—
217	C₂×M₁₆	—	4	1	no	—
218	C₂×M₁₆	C₅×Q₈	1	4	yes	complemented
219	C₂²×C₈	—	2	2	no	—
220	C₂²×C₈	—	4	1	no	—
221	C₂²×C₈	—	4	1	no	—
222	C₂²×C₈	C₂³×C₅	1	2	yes	—
223	C₂²×C₈	C₂³×C₅	1	2	yes	—
224	C₂²×C₈	C₂³×C₅	1	2	yes	—
225	C₂²×C₈	C₂³×C₅	1	2	yes	—
226	C₄×Q₈	—	4	1	no	—
227	C₄×Q₈	—	4	1	no	—
228	#117	—	4	1	no	—
229	#117	—	4	1	no	—
230	C₂×C₄⋊C₄	C₂×C₄×C₅	1	2	yes	—
231	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
232	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
233	C₂×C₄⋊C₄	C₂×C₄×C₅	1	2	yes	—
234	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
235	C₂×C₄⋊C₄	C₂×C₄×C₅	1	2	yes	—
236	C₂×C₄⋊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	1	yes	characteristic
239	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
240	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	2	yes	—
241	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
242	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
243	C₂×C₄²	C₂³×C₅	1	2	yes	—
244	C₂×C₄²	C₂³×C₅	1	2	yes	—
245	C₄⋊C₈	—	4	2	no	—
246	C₄⋊C₈	—	4	1	no	—
247	C₄⋊C₈	—	4	1	no	—
248	C₄⋊C₈	—	4	2	no	—
249	C₂²⋊C₈	—	2	4	no	—
250	#97	—	4	2	no	—
251	C₄×C₈	—	4	2	no	—
252	#95	C₂×C₄×C₅	1	2	yes	—
253	#95	C₂×C₄×C₅	1	2	yes	—
254	#95	C₂×C₄×C₅	1	2	yes	—
255	#95	C₂×C₄×C₅	1	1	yes	characteristic
256	#95	C₂×C₄×C₅	1	1	yes	characteristic
257	#95	C₂×C₄×C₅	1	2	yes	—
258	C₂²×C₅	—	2	2	no	—
259	C₂²×C₅	—	2	4	no	—
260	C₂²×C₅	—	4	1	no	—
261	C₂²×C₅	—	4	1	no	—
262	C₂²×C₅	—	4	2	no	—
263	C₂²×C₅	C₂×C₄×Q₈	1	1	yes	characteristic
264	C₂²×C₅	#518	1	1	yes	characteristic
265	C₂²×C₅	#520	1	1	yes	characteristic
266	C₂²×C₅	C₂×#131	1	2	yes	—
267	C₂²×C₅	#568	1	2	yes	—
268	C₄×C₅	—	2	2	no	—
269	C₄×C₅	—	2	4	no	—
270	C₄×C₅	—	4	1	no	—
271	C₄×C₅	—	4	1	no	—
272	C₄×C₅	—	4	1	no	—
273	C₄×C₅	—	4	1	no	—
274	C₄×C₅	—	4	2	no	—
275	C₄×C₅	—	4	2	no	—
276	C₄×C₅	—	4	2	no	—
277	C₄×C₅	#538	1	1	yes	characteristic
278	C₄×C₅	#539	1	1	yes	characteristic
279	C₄×C₅	#543	1	1	yes	characteristic
280	C₄×C₅	#544	1	1	yes	characteristic
281	C₂⁴	C₂²×C₄×C₅	1	1	yes	characteristic
282	C₂×Q₈	—	2	4	no	—
283	C₂×Q₈	—	4	1	no	—
284	C₂²×C₄	—	2	1	no	—
285	C₂²×C₄	—	2	1	no	—
286	C₂²×C₄	—	2	1	no	—
287	C₂²×C₄	—	2	1	no	—
288	C₂²×C₄	C₂²×C₄×C₅	1	2	yes	—
289	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
290	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
291	C₂²×C₄	C₂²×C₄×C₅	1	2	yes	—
292	C₂²×C₄	C₂²×C₄×C₅	1	2	yes	—
293	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
294	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
295	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
296	C₂²×C₄	C₂²×C₄×C₅	1	2	yes	—
297	C₂²×C₄	C₂×C₅×Q₈	1	2	yes	—
298	C₂²×C₄	C₅×#41	1	2	yes	—
299	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
300	M₁₆	—	4	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	—	2	2	no	—
309	C₂×C₈	—	2	2	no	—
310	C₂×C₈	—	2	2	no	—
311	C₂×C₈	—	2	2	no	—
312	C₂×C₈	—	4	4	no	—
313	C₂×C₈	C₂×C₅×Q₈	1	4	yes	—
314	C₄⋊C₄	—	2	4	no	—
315	C₄⋊C₄	—	4	1	no	—
316	C₄⋊C₄	—	4	1	no	—
317	C₄⋊C₄	—	4	2	no	—
318	C₄⋊C₄	—	4	1	no	—
319	C₄⋊C₄	—	4	2	no	—
320	C₄⋊C₄	—	4	2	no	—
321	C₂²⋊C₄	—	2	4	no	—
322	C₂²⋊C₄	—	4	1	no	—
323	C₂²⋊C₄	—	4	1	no	—
324	C₂²⋊C₄	—	4	2	no	—
325	C₄²	—	2	2	no	—
326	C₄²	—	2	2	no	—
327	C₄²	—	2	1	no	—
328	C₄²	—	2	1	no	—
329	C₄²	—	2	2	no	—
330	C₄²	—	2	1	no	—
331	C₄²	—	2	1	no	—
332	C₄²	—	2	2	no	—
333	C₂×C₅	—	4	2	no	—
334	C₂×C₅	#2329	1	1	yes	characteristic
335	C₂×C₅	#2962	1	2	yes	—
336	C₂×C₅	#2977	1	1	yes	characteristic
337	C₂×C₅	#2980	1	1	yes	characteristic
338	C₂×C₅	#2993	1	2	yes	—
339	C₂³	—	2	1	no	—
340	C₂³	—	2	1	no	—
341	C₂³	—	2	2	no	—
342	C₂³	—	2	2	no	—
343	C₂³	C₄×C₅×Q₈	1	2	yes	—
344	C₂³	C₂³×C₄×C₅	1	1	yes	characteristic
345	Q₈	—	4	4	no	—
346	C₂×C₄	—	2	2	no	—
347	C₂×C₄	—	2	1	no	—
348	C₂×C₄	—	2	1	no	—
349	C₂×C₄	—	2	2	no	—
350	C₂×C₄	—	2	2	no	—
351	C₂×C₄	—	2	2	no	—
352	C₂×C₄	—	2	2	no	—
353	C₂×C₄	—	2	2	no	—
354	C₂×C₄	—	2	1	no	—
355	C₂×C₄	—	2	1	no	—
356	C₂×C₄	—	2	1	no	—
357	C₂×C₄	—	2	1	no	—
358	C₂×C₄	—	2	2	no	—
359	C₂×C₄	—	2	2	no	—
360	C₂×C₄	—	2	2	no	—
361	C₂×C₄	—	2	2	no	—
362	C₂×C₄	—	2	2	no	—
363	C₂×C₄	—	2	2	no	—
364	C₂×C₄	—	2	2	no	—
365	C₂×C₄	—	2	2	no	—
366	C₂×C₄	—	2	2	no	—
367	C₂×C₄	—	2	2	no	—
368	C₂×C₄	—	2	2	no	—
369	C₂×C₄	—	2	2	no	—
370	C₂×C₄	—	2	2	no	—
371	C₂×C₄	C₄×C₅×Q₈	1	2	yes	—
372	C₂×C₄	C₅×#131	1	4	yes	—
373	C₂×C₄	C₂²×C₅×Q₈	1	1	yes	characteristic
374	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
375	C₂×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
376	C₂×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
377	C₂×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
378	C₂×C₄	C₅×2₋¹⁺⁴	1	1	yes	characteristic
379	C₈	—	2	4	no	—
380	C₈	—	4	2	no	—
381	C₈	—	4	2	no	—
382	C₈	—	4	2	no	—
383	C₅	#22290	1	1	yes	characteristic, direct product factor, Sylow
384	C₂²	—	2	2	no	—
385	C₂²	—	2	4	no	—
386	C₂²	—	4	2	no	—
387	C₂²	—	4	1	no	—
388	C₂²	—	4	1	no	—
389	C₂²	C₂×C₄×C₅×Q₈	1	1	yes	characteristic
390	C₂²	C₅×#518	1	1	yes	characteristic
391	C₂²	C₅×#520	1	1	yes	characteristic
392	C₂²	C₂×C₅×#131	1	2	yes	—
393	C₂²	C₅×#568	1	2	yes	—
394	C₄	—	2	2	no	—
395	C₄	—	2	4	no	—
396	C₄	—	4	2	no	—
397	C₄	—	4	2	no	—
398	C₄	—	4	1	no	—
399	C₄	—	4	1	no	—
400	C₄	—	4	1	no	—
401	C₄	—	4	1	no	—
402	C₄	—	4	2	no	—
403	C₄	C₅×#538	1	1	yes	characteristic
404	C₄	C₅×#539	1	1	yes	characteristic
405	C₄	C₅×#543	1	1	yes	characteristic
406	C₄	C₅×#544	1	1	yes	characteristic
407	C₂	—	4	2	no	—
408	C₂	C₅×#2329	1	1	yes	characteristic
409	C₂	C₅×#2962	1	2	yes	—
410	C₂	C₅×#2977	1	1	yes	characteristic
411	C₂	C₅×#2980	1	1	yes	characteristic
412	C₂	C₅×#2993	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	C₂⁴×C₅	C₂²×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
2. C₅×#1984	C₂	semidirect
3. C₅×#1940	C₂	semidirect
4. C₅×#1917	C₂	semidirect
5. C₅×#1916	C₂	semidirect
37. #22290	C₅	direct (N × H)
42. C₂×C₅×M₁₆	Q₈	semidirect
83. #1984	C₂×C₅	semidirect
84. #1940	C₂×C₅	semidirect
85. #1917	C₂×C₅	semidirect
86. #1916	C₂×C₅	semidirect
218. C₂×M₁₆	C₅×Q₈	semidirect
383. C₅	#22290	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×#2396	2
C₅×#1984	2
C₅×#1940	2
C₅×#1917	2
C₅×#1916	2
C₅×#1850	2
C₅×#1798	2
C₅×#1753	2
C₅×#1729	2
#22290	5

Subgroups — C5×#22290 #11945010

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#22290 #11945010