Subgroups — C₅×#22289 #11945009

Order 1280.

754 conjugacy classes of subgroups.

The subgroup lattice has 456 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₅×C₂²⋊Q₈	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×#1851	C₂	1	2	yes	maximal
7	C₅×#1797	C₂	1	1	yes	maximal, characteristic
8	C₅×#1753	C₂	1	2	yes	maximal
9	C₅×#1728	C₂	1	1	yes	maximal, characteristic
10	C₂²×C₅×M₁₆	C₂²	1	1	yes	characteristic
11	C₂²×C₅×M₁₆	C₂²	1	1	yes	characteristic
12	C₂×C₅×C₂²⋊Q₈	C₄	1	1	yes	characteristic
13	C₂×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
14	C₂²×C₄²×C₅	C₂²	1	1	yes	characteristic
15	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
16	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
17	C₂×C₅×C₄⋊C₈	C₂²	1	2	yes	—
18	C₂×C₅×C₄⋊C₈	C₂²	1	2	yes	—
19	C₂×C₅×C₂²⋊C₈	C₂²	1	2	yes	—
20	C₂×C₅×#97	C₂²	1	2	yes	—
21	C₂×C₄×C₅×C₈	C₂²	1	2	yes	—
22	C₅×#391	C₄	1	1	yes	characteristic
23	C₅×#389	C₄	1	1	yes	characteristic
24	C₅×#387	C₄	1	2	yes	—
25	C₅×#385	C₄	1	2	yes	—
26	C₅×#380	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	#22289	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
38	C₂²×C₅×Q₈	C₂×C₄	1	1	yes	characteristic
39	C₂³×C₄×C₅	C₂×C₄	1	1	yes	characteristic
40	C₂³×C₄×C₅	C₂×C₄	1	1	yes	characteristic
41	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
42	C₂×C₅×M₁₆	—	2	2	no	—
43	C₂×C₅×M₁₆	—	4	1	no	—
44	C₂×C₅×M₁₆	—	4	1	no	—
45	C₂×C₅×M₁₆	—	4	1	no	—
46	C₂×C₅×M₁₆	—	4	1	no	—
47	C₂×C₅×M₁₆	Q₈	1	4	yes	complemented
48	C₂²×C₅×C₈	C₂³	1	2	yes	—
49	C₂²×C₅×C₈	C₂³	1	2	yes	—
50	C₂²×C₅×C₈	C₂³	1	2	yes	—
51	C₂²×C₅×C₈	C₂³	1	2	yes	—
52	C₅×C₂²⋊Q₈	—	2	4	no	—
53	C₄×C₅×Q₈	—	4	1	no	—
54	C₄×C₅×Q₈	—	4	1	no	—
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	1	yes	characteristic
59	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
60	C₂×C₅×C₄⋊C₄	C₂×C₄	1	2	yes	—
61	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	2	yes	—
62	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	2	yes	—
63	C₂×C₄²×C₅	—	4	1	no	—
64	C₂×C₄²×C₅	—	4	1	no	—
65	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
66	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
67	C₂×C₄²×C₅	C₂³	1	2	yes	—
68	C₂×C₄²×C₅	C₂³	1	2	yes	—
69	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
70	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
71	C₅×C₄⋊C₈	—	4	1	no	—
72	C₅×C₄⋊C₈	—	4	1	no	—
73	C₅×C₄⋊C₈	—	4	2	no	—
74	C₅×C₄⋊C₈	—	4	2	no	—
75	C₅×C₂²⋊C₈	—	2	4	no	—
76	C₅×#97	—	4	2	no	—
77	C₄×C₅×C₈	—	4	2	no	—
78	C₅×#95	C₂×C₄	1	2	yes	—
79	C₅×#95	C₂×C₄	1	2	yes	—
80	C₅×#95	C₂×C₄	1	2	yes	—
81	C₅×#95	C₂×C₄	1	2	yes	—
82	C₅×#95	C₂×C₄	1	2	yes	—
83	C₄×C₂²⋊Q₈	C₂×C₅	1	1	yes	characteristic
84	#1984	C₂×C₅	1	2	yes	complemented
85	#1940	C₂×C₅	1	2	yes	complemented
86	#1917	C₂×C₅	1	2	yes	complemented
87	#1916	C₂×C₅	1	2	yes	complemented
88	#1851	C₂×C₅	1	2	yes	—
89	#1797	C₂×C₅	1	1	yes	characteristic
90	#1753	C₂×C₅	1	2	yes	—
91	#1728	C₂×C₅	1	1	yes	characteristic
92	C₂⁴×C₅	C₂²×C₄	1	1	yes	characteristic
93	C₂×C₅×Q₈	—	4	1	no	—
94	C₂×C₅×Q₈	—	4	1	no	—
95	C₂×C₅×Q₈	M₁₆	1	4	yes	complemented
96	C₂²×C₄×C₅	—	2	1	no	—
97	C₂²×C₄×C₅	—	2	1	no	—
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	—	4	1	no	—
103	C₂²×C₄×C₅	—	4	1	no	—
104	C₂²×C₄×C₅	—	4	1	no	—
105	C₂²×C₄×C₅	—	4	1	no	—
106	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
107	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
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	1	yes	characteristic
113	C₂²×C₄×C₅	C₂²×C₄	1	2	yes	—
114	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
115	C₂²×C₄×C₅	C₂×Q₈	1	2	yes	—
116	C₂²×C₄×C₅	#41	1	2	yes	—
117	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
118	C₅×M₁₆	—	4	4	no	—
119	C₅×M₁₆	—	4	4	no	—
120	C₂×C₅×C₈	—	2	2	no	—
121	C₂×C₅×C₈	—	2	2	no	—
122	C₂×C₅×C₈	—	2	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	—	2	2	no	—
129	C₂×C₅×C₈	—	2	2	no	—
130	C₂×C₅×C₈	—	2	2	no	—
131	C₂×C₅×C₈	C₂×Q₈	1	4	yes	—
132	C₅×C₄⋊C₄	—	2	2	no	—
133	C₅×C₄⋊C₄	—	2	4	no	—
134	C₅×C₄⋊C₄	—	2	4	no	—
135	C₅×C₄⋊C₄	—	4	1	no	—
136	C₅×C₄⋊C₄	—	4	1	no	—
137	C₅×C₄⋊C₄	—	4	2	no	—
138	C₅×C₂²⋊C₄	—	2	4	no	—
139	C₅×C₂²⋊C₄	—	4	2	no	—
140	C₄²×C₅	—	2	1	no	—
141	C₄²×C₅	—	2	1	no	—
142	C₄²×C₅	—	2	1	no	—
143	C₄²×C₅	—	2	1	no	—
144	C₄²×C₅	—	2	2	no	—
145	C₄²×C₅	—	2	2	no	—
146	C₄²×C₅	—	2	2	no	—
147	C₄²×C₅	—	2	2	no	—
148	C₄²×C₅	—	4	1	no	—
149	C₄²×C₅	—	4	1	no	—
150	C₂²×M₁₆	C₂²×C₅	1	1	yes	characteristic
151	C₂²×M₁₆	C₂²×C₅	1	1	yes	characteristic
152	C₂×C₂²⋊Q₈	C₄×C₅	1	1	yes	characteristic
153	C₂×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
154	C₂²×C₄²	C₂²×C₅	1	1	yes	characteristic
155	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
156	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
157	C₂×C₄⋊C₈	C₂²×C₅	1	2	yes	—
158	C₂×C₄⋊C₈	C₂²×C₅	1	2	yes	—
159	C₂×C₂²⋊C₈	C₂²×C₅	1	2	yes	—
160	C₂×#97	C₂²×C₅	1	2	yes	—
161	C₂×C₄×C₈	C₂²×C₅	1	2	yes	—
162	#391	C₄×C₅	1	1	yes	characteristic
163	#389	C₄×C₅	1	1	yes	characteristic
164	#387	C₄×C₅	1	2	yes	—
165	#385	C₄×C₅	1	2	yes	—
166	#380	C₄×C₅	1	1	yes	characteristic
167	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	—
168	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
169	C₄×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
170	#336	C₂²×C₅	1	2	yes	—
171	#336	C₂²×C₅	1	2	yes	—
172	#336	C₂²×C₅	1	2	yes	—
173	#336	C₂²×C₅	1	2	yes	—
174	#336	C₂²×C₅	1	2	yes	—
175	#336	C₂²×C₅	1	2	yes	—
176	#336	C₂²×C₅	1	2	yes	—
177	C₂³×C₅	—	2	1	no	—
178	C₂³×C₅	—	2	1	no	—
179	C₂³×C₅	—	2	1	no	—
180	C₂³×C₅	—	2	1	no	—
181	C₂³×C₅	—	2	1	no	—
182	C₂³×C₅	—	2	1	no	—
183	C₂³×C₅	C₄×Q₈	1	2	yes	—
184	C₂³×C₅	C₂³×C₄	1	1	yes	characteristic
185	C₅×Q₈	—	4	4	no	—
186	C₂×C₄×C₅	—	2	1	no	—
187	C₂×C₄×C₅	—	2	1	no	—
188	C₂×C₄×C₅	—	2	2	no	—
189	C₂×C₄×C₅	—	2	1	no	—
190	C₂×C₄×C₅	—	2	1	no	—
191	C₂×C₄×C₅	—	2	1	no	—
192	C₂×C₄×C₅	—	2	1	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	1	no	—
199	C₂×C₄×C₅	—	2	1	no	—
200	C₂×C₄×C₅	—	2	2	no	—
201	C₂×C₄×C₅	—	2	2	no	—
202	C₂×C₄×C₅	—	2	2	no	—
203	C₂×C₄×C₅	—	2	2	no	—
204	C₂×C₄×C₅	—	2	1	no	—
205	C₂×C₄×C₅	—	2	2	no	—
206	C₂×C₄×C₅	—	2	2	no	—
207	C₂×C₄×C₅	—	2	1	no	—
208	C₂×C₄×C₅	—	2	2	no	—
209	C₂×C₄×C₅	—	2	2	no	—
210	C₂×C₄×C₅	—	2	2	no	—
211	C₂×C₄×C₅	—	2	1	no	—
212	C₂×C₄×C₅	—	2	1	no	—
213	C₂×C₄×C₅	—	4	4	no	—
214	C₂×C₄×C₅	—	4	4	no	—
215	C₂×C₄×C₅	C₄×Q₈	1	2	yes	—
216	C₂×C₄×C₅	C₂×M₁₆	1	4	yes	—
217	C₂×C₄×C₅	C₂×M₁₆	1	2	yes	—
218	C₂×C₄×C₅	#131	1	2	yes	—
219	C₂×C₄×C₅	C₂²×Q₈	1	1	yes	characteristic
220	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
221	C₂×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
222	C₂×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
223	C₂×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
224	C₂×C₄×C₅	2₋¹⁺⁴	1	1	yes	characteristic
225	C₅×C₈	—	2	4	no	—
226	C₅×C₈	—	4	2	no	—
227	C₅×C₈	—	4	2	no	—
228	C₅×C₈	—	4	2	no	—
229	C₂²×Q₈	C₂×C₄×C₅	1	1	yes	characteristic
230	C₂³×C₄	C₂×C₄×C₅	1	1	yes	characteristic
231	C₂³×C₄	C₂×C₄×C₅	1	1	yes	characteristic
232	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
233	C₂×M₁₆	—	2	2	no	—
234	C₂×M₁₆	—	4	1	no	—
235	C₂×M₁₆	—	4	1	no	—
236	C₂×M₁₆	—	4	1	no	—
237	C₂×M₁₆	—	4	1	no	—
238	C₂×M₁₆	C₅×Q₈	1	4	yes	complemented
239	C₂²×C₈	C₂³×C₅	1	2	yes	—
240	C₂²×C₈	C₂³×C₅	1	2	yes	—
241	C₂²×C₈	C₂³×C₅	1	2	yes	—
242	C₂²×C₈	C₂³×C₅	1	2	yes	—
243	C₂²⋊Q₈	—	2	4	no	—
244	C₄×Q₈	—	4	1	no	—
245	C₄×Q₈	—	4	1	no	—
246	C₂×C₄⋊C₄	C₂×C₄×C₅	1	2	yes	—
247	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
248	C₂×C₄⋊C₄	C₂×C₄×C₅	1	2	yes	—
249	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
250	C₂×C₄⋊C₄	C₂×C₄×C₅	1	2	yes	—
251	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
252	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	2	yes	—
253	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	2	yes	—
254	C₂×C₄²	—	4	1	no	—
255	C₂×C₄²	—	4	1	no	—
256	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
257	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
258	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
259	C₂×C₄²	C₂³×C₅	1	2	yes	—
260	C₂×C₄²	C₂³×C₅	1	2	yes	—
261	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
262	C₄⋊C₈	—	4	2	no	—
263	C₄⋊C₈	—	4	1	no	—
264	C₄⋊C₈	—	4	1	no	—
265	C₄⋊C₈	—	4	2	no	—
266	C₂²⋊C₈	—	2	4	no	—
267	#97	—	4	2	no	—
268	C₄×C₈	—	4	2	no	—
269	#95	C₂×C₄×C₅	1	2	yes	—
270	#95	C₂×C₄×C₅	1	2	yes	—
271	#95	C₂×C₄×C₅	1	2	yes	—
272	#95	C₂×C₄×C₅	1	2	yes	—
273	#95	C₂×C₄×C₅	1	2	yes	—
274	C₂²×C₅	—	2	2	no	—
275	C₂²×C₅	—	2	2	no	—
276	C₂²×C₅	—	2	2	no	—
277	C₂²×C₅	—	4	1	no	—
278	C₂²×C₅	—	4	1	no	—
279	C₂²×C₅	—	4	1	no	—
280	C₂²×C₅	—	4	1	no	—
281	C₂²×C₅	C₂×C₄×Q₈	1	1	yes	characteristic
282	C₂²×C₅	#518	1	1	yes	characteristic
283	C₂²×C₅	#520	1	1	yes	characteristic
284	C₂²×C₅	C₂²×M₁₆	1	1	yes	characteristic
285	C₂²×C₅	C₂×#131	1	1	yes	characteristic
286	C₂²×C₅	#568	1	1	yes	characteristic
287	C₂²×C₅	#568	1	1	yes	characteristic
288	C₄×C₅	—	2	2	no	—
289	C₄×C₅	—	2	2	no	—
290	C₄×C₅	—	2	4	no	—
291	C₄×C₅	—	2	2	no	—
292	C₄×C₅	—	4	1	no	—
293	C₄×C₅	—	4	2	no	—
294	C₄×C₅	—	4	1	no	—
295	C₄×C₅	—	4	2	no	—
296	C₄×C₅	—	4	2	no	—
297	C₄×C₅	#538	1	1	yes	characteristic
298	C₄×C₅	#539	1	1	yes	characteristic
299	C₄×C₅	#543	1	1	yes	characteristic
300	C₄×C₅	#544	1	1	yes	characteristic
301	C₂⁴	C₂²×C₄×C₅	1	1	yes	characteristic
302	C₂×Q₈	—	4	1	no	—
303	C₂×Q₈	—	4	1	no	—
304	C₂×Q₈	C₅×M₁₆	1	4	yes	complemented
305	C₂²×C₄	—	2	1	no	—
306	C₂²×C₄	—	2	1	no	—
307	C₂²×C₄	—	2	1	no	—
308	C₂²×C₄	—	2	1	no	—
309	C₂²×C₄	—	2	2	no	—
310	C₂²×C₄	—	2	2	no	—
311	C₂²×C₄	—	4	1	no	—
312	C₂²×C₄	—	4	1	no	—
313	C₂²×C₄	—	4	1	no	—
314	C₂²×C₄	—	4	1	no	—
315	C₂²×C₄	C₂²×C₄×C₅	1	2	yes	—
316	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
317	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
318	C₂²×C₄	C₂²×C₄×C₅	1	2	yes	—
319	C₂²×C₄	C₂²×C₄×C₅	1	2	yes	—
320	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
321	C₂²×C₄	C₂²×C₄×C₅	1	2	yes	—
322	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
323	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
324	C₂²×C₄	C₂×C₅×Q₈	1	2	yes	—
325	C₂²×C₄	C₅×#41	1	2	yes	—
326	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
327	M₁₆	—	4	4	no	—
328	M₁₆	—	4	4	no	—
329	C₂×C₈	—	2	2	no	—
330	C₂×C₈	—	2	2	no	—
331	C₂×C₈	—	2	2	no	—
332	C₂×C₈	—	2	2	no	—
333	C₂×C₈	—	2	2	no	—
334	C₂×C₈	—	2	2	no	—
335	C₂×C₈	—	2	2	no	—
336	C₂×C₈	—	2	2	no	—
337	C₂×C₈	—	2	2	no	—
338	C₂×C₈	—	2	2	no	—
339	C₂×C₈	—	2	2	no	—
340	C₂×C₈	C₂×C₅×Q₈	1	4	yes	—
341	C₄⋊C₄	—	2	2	no	—
342	C₄⋊C₄	—	2	4	no	—
343	C₄⋊C₄	—	2	4	no	—
344	C₄⋊C₄	—	4	1	no	—
345	C₄⋊C₄	—	4	2	no	—
346	C₄⋊C₄	—	4	1	no	—
347	C₂²⋊C₄	—	2	4	no	—
348	C₂²⋊C₄	—	4	2	no	—
349	C₄²	—	2	2	no	—
350	C₄²	—	2	2	no	—
351	C₄²	—	2	1	no	—
352	C₄²	—	2	1	no	—
353	C₄²	—	2	2	no	—
354	C₄²	—	2	1	no	—
355	C₄²	—	2	1	no	—
356	C₄²	—	2	2	no	—
357	C₄²	—	4	1	no	—
358	C₄²	—	4	1	no	—
359	C₂×C₅	—	4	2	no	—
360	C₂×C₅	#2329	1	1	yes	characteristic
361	C₂×C₅	#2962	1	1	yes	characteristic
362	C₂×C₅	Q₈×M₁₆	1	1	yes	characteristic
363	C₂×C₅	#2973	1	1	yes	characteristic
364	C₂×C₅	#2976	1	1	yes	characteristic
365	C₂×C₅	#2991	1	1	yes	characteristic
366	C₂×C₅	#2995	1	1	yes	characteristic
367	C₂³	—	2	1	no	—
368	C₂³	—	2	1	no	—
369	C₂³	—	2	1	no	—
370	C₂³	—	2	1	no	—
371	C₂³	—	2	1	no	—
372	C₂³	—	2	1	no	—
373	C₂³	C₄×C₅×Q₈	1	2	yes	—
374	C₂³	C₂³×C₄×C₅	1	1	yes	characteristic
375	Q₈	—	4	4	no	—
376	C₂×C₄	—	2	1	no	—
377	C₂×C₄	—	2	1	no	—
378	C₂×C₄	—	2	2	no	—
379	C₂×C₄	—	2	1	no	—
380	C₂×C₄	—	2	1	no	—
381	C₂×C₄	—	2	1	no	—
382	C₂×C₄	—	2	1	no	—
383	C₂×C₄	—	2	2	no	—
384	C₂×C₄	—	2	2	no	—
385	C₂×C₄	—	2	2	no	—
386	C₂×C₄	—	2	2	no	—
387	C₂×C₄	—	2	2	no	—
388	C₂×C₄	—	2	1	no	—
389	C₂×C₄	—	2	1	no	—
390	C₂×C₄	—	2	2	no	—
391	C₂×C₄	—	2	2	no	—
392	C₂×C₄	—	2	2	no	—
393	C₂×C₄	—	2	2	no	—
394	C₂×C₄	—	2	1	no	—
395	C₂×C₄	—	2	2	no	—
396	C₂×C₄	—	2	2	no	—
397	C₂×C₄	—	2	1	no	—
398	C₂×C₄	—	2	2	no	—
399	C₂×C₄	—	2	2	no	—
400	C₂×C₄	—	2	2	no	—
401	C₂×C₄	—	2	1	no	—
402	C₂×C₄	—	2	1	no	—
403	C₂×C₄	—	4	4	no	—
404	C₂×C₄	—	4	4	no	—
405	C₂×C₄	C₄×C₅×Q₈	1	2	yes	—
406	C₂×C₄	C₂×C₅×M₁₆	1	4	yes	—
407	C₂×C₄	C₂×C₅×M₁₆	1	2	yes	—
408	C₂×C₄	C₅×#131	1	2	yes	—
409	C₂×C₄	C₂²×C₅×Q₈	1	1	yes	characteristic
410	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
411	C₂×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
412	C₂×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
413	C₂×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
414	C₂×C₄	C₅×2₋¹⁺⁴	1	1	yes	characteristic
415	C₈	—	2	4	no	—
416	C₈	—	4	2	no	—
417	C₈	—	4	2	no	—
418	C₈	—	4	2	no	—
419	C₅	#22289	1	1	yes	characteristic, direct product factor, Sylow
420	C₂²	—	2	2	no	—
421	C₂²	—	2	2	no	—
422	C₂²	—	2	2	no	—
423	C₂²	—	4	1	no	—
424	C₂²	—	4	1	no	—
425	C₂²	—	4	1	no	—
426	C₂²	—	4	1	no	—
427	C₂²	C₂×C₄×C₅×Q₈	1	1	yes	characteristic
428	C₂²	C₅×#518	1	1	yes	characteristic
429	C₂²	C₅×#520	1	1	yes	characteristic
430	C₂²	C₂²×C₅×M₁₆	1	1	yes	characteristic
431	C₂²	C₂×C₅×#131	1	1	yes	characteristic
432	C₂²	C₅×#568	1	1	yes	characteristic
433	C₂²	C₅×#568	1	1	yes	characteristic
434	C₄	—	2	2	no	—
435	C₄	—	2	2	no	—
436	C₄	—	2	4	no	—
437	C₄	—	2	2	no	—
438	C₄	—	4	2	no	—
439	C₄	—	4	2	no	—
440	C₄	—	4	1	no	—
441	C₄	—	4	1	no	—
442	C₄	—	4	2	no	—
443	C₄	C₅×#538	1	1	yes	characteristic
444	C₄	C₅×#539	1	1	yes	characteristic
445	C₄	C₅×#543	1	1	yes	characteristic
446	C₄	C₅×#544	1	1	yes	characteristic
447	C₂	—	4	2	no	—
448	C₂	C₅×#2329	1	1	yes	characteristic
449	C₂	C₅×#2962	1	1	yes	characteristic
450	C₂	C₅×Q₈×M₁₆	1	1	yes	characteristic
451	C₂	C₅×#2973	1	1	yes	characteristic
452	C₂	C₅×#2976	1	1	yes	characteristic
453	C₂	C₅×#2991	1	1	yes	characteristic
454	C₂	C₅×#2995	1	1	yes	characteristic

	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. #22289	C₅	direct (N × H)
47. C₂×C₅×M₁₆	Q₈	semidirect
84. #1984	C₂×C₅	semidirect
85. #1940	C₂×C₅	semidirect
86. #1917	C₂×C₅	semidirect
87. #1916	C₂×C₅	semidirect
95. C₂×C₅×Q₈	M₁₆	semidirect
238. C₂×M₁₆	C₅×Q₈	semidirect
304. C₂×Q₈	C₅×M₁₆	semidirect
419. C₅	#22289	direct (N × H)

Maximal subgroups

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

subgroup	index
C₄×C₅×C₂²⋊Q₈	2
C₅×#1984	2
C₅×#1940	2
C₅×#1917	2
C₅×#1916	2
C₅×#1851	2
C₅×#1797	2
C₅×#1753	2
C₅×#1728	2
#22289	5

Subgroups — C5×#22289 #11945009

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#22289 #11945009