Subgroups — C₅×#22713 #11945433

Order 1280.

950 conjugacy classes of subgroups.

The subgroup lattice has 470 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
2	C₅×#2354	C₂	1	1	yes	maximal, characteristic
3	C₅×D₄×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic
4	C₅×#1948	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#1947	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#1854	C₂	1	2	yes	maximal, complemented
7	C₅×#1852	C₂	1	2	yes	maximal, complemented
8	C₅×#1834	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#1809	C₂	1	2	yes	maximal, complemented
10	C₄×C₅×#107	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#1736	C₂	1	2	yes	maximal, complemented
12	C₂²×C₅×M₁₆	C₂²	1	2	yes	—
13	C₂×C₄×C₅×D₄	—	2	1	no	—
14	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
15	C₂×C₅×#117	C₂²	1	2	yes	—
16	C₂²×C₅×C₄⋊C₄	C₂²	1	2	yes	—
17	C₅×#436	C₄	1	8	yes	complemented
18	C₂×C₅×#107	C₂²	1	1	yes	characteristic
19	C₂×C₅×#107	C₂²	1	1	yes	characteristic
20	C₂×C₅×#107	C₂²	1	2	yes	—
21	C₂×C₅×#106	C₂²	1	2	yes	—
22	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
23	C₂×C₅×C₂²⋊C₈	C₂²	1	2	yes	—
24	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
25	C₅×#390	—	2	1	no	—
26	C₅×#389	—	2	1	no	—
27	C₅×#388	—	2	2	no	—
28	C₅×#385	—	2	2	no	—
29	C₅×#384	C₂²	1	1	yes	characteristic
30	C₅×#384	C₂²	1	1	yes	characteristic
31	C₅×#380	C₂²	1	2	yes	—
32	C₅×#380	C₂²	1	2	yes	—
33	C₄×C₅×C₄⋊C₄	—	2	1	no	—
34	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
35	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
36	C₅×#340	C₂²	1	1	yes	characteristic
37	C₅×#340	C₂²	1	1	yes	characteristic
38	C₅×#340	C₂²	1	2	yes	—
39	C₅×#340	C₂²	1	2	yes	—
40	C₅×#340	C₂²	1	2	yes	—
41	C₅×#340	C₂²	1	2	yes	—
42	#22713	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
43	C₂²×C₅×D₄	D₄	1	1	yes	characteristic
44	C₂³×C₄×C₅	—	2	2	no	—
45	C₂³×C₄×C₅	C₂³	1	2	yes	—
46	C₂×C₅×M₁₆	—	4	2	no	—
47	C₂×C₅×M₁₆	—	4	2	no	—
48	C₂×C₅×M₁₆	C₂×C₄	1	8	yes	complemented
49	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
50	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
51	C₂²×C₅×C₈	C₂³	1	2	yes	—
52	C₄×C₅×D₄	—	4	4	no	—
53	C₄×C₅×D₄	C₂×C₄	1	4	yes	—
54	C₄×C₅×D₄	Q₈	1	4	yes	—
55	C₅×#117	—	2	4	no	—
56	C₅×#117	—	4	2	no	—
57	C₂×C₅×C₄⋊C₄	—	2	4	no	—
58	C₂×C₅×C₄⋊C₄	—	2	1	no	—
59	C₂×C₅×C₄⋊C₄	—	2	1	no	—
60	C₂×C₅×C₄⋊C₄	—	2	2	no	—
61	C₂×C₅×C₄⋊C₄	—	2	1	no	—
62	C₂×C₅×C₄⋊C₄	—	2	1	no	—
63	C₂×C₅×C₄⋊C₄	—	4	2	no	—
64	C₂×C₅×C₄⋊C₄	D₄	1	1	yes	characteristic
65	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
66	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
67	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
68	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
69	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
70	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
71	C₂×C₅×C₂²⋊C₄	—	2	2	no	—
72	C₂×C₅×C₂²⋊C₄	—	2	2	no	—
73	C₂×C₅×C₂²⋊C₄	—	2	2	no	—
74	C₂×C₅×C₂²⋊C₄	D₄	1	2	yes	—
75	C₂×C₄²×C₅	—	2	1	no	—
76	C₂×C₄²×C₅	—	2	2	no	—
77	C₂×C₄²×C₅	—	2	1	no	—
78	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
79	C₅×#107	—	2	2	no	—
80	C₅×#107	—	2	2	no	—
81	C₅×#107	—	4	2	no	—
82	C₅×#106	—	4	2	no	—
83	C₅×C₄⋊C₈	C₂×C₄	1	4	yes	complemented
84	C₅×C₂²⋊C₈	C₂×C₄	1	8	yes	complemented
85	C₄×C₅×C₈	C₂×C₄	1	4	yes	complemented
86	C₅×#95	—	2	2	no	—
87	C₅×#95	—	2	1	no	—
88	C₅×#95	—	2	1	no	—
89	C₅×#95	—	2	2	no	—
90	C₂×#436	C₂×C₅	1	1	yes	characteristic
91	#2354	C₂×C₅	1	1	yes	characteristic
92	D₄×C₄⋊C₄	C₂×C₅	1	1	yes	characteristic
93	#1948	C₂×C₅	1	1	yes	characteristic, complemented
94	#1947	C₂×C₅	1	1	yes	characteristic, complemented
95	#1854	C₂×C₅	1	2	yes	complemented
96	#1852	C₂×C₅	1	2	yes	complemented
97	#1834	C₂×C₅	1	1	yes	characteristic, complemented
98	#1809	C₂×C₅	1	2	yes	complemented
99	C₄×#107	C₂×C₅	1	1	yes	characteristic, complemented
100	#1736	C₂×C₅	1	2	yes	complemented
101	C₂⁴×C₅	C₂×D₄	1	2	yes	—
102	C₂×C₅×D₄	—	2	2	no	—
103	C₂×C₅×D₄	—	2	2	no	—
104	C₂×C₅×D₄	C₄⋊C₄	1	4	yes	—
105	C₂²×C₄×C₅	—	2	2	no	—
106	C₂²×C₄×C₅	—	2	2	no	—
107	C₂²×C₄×C₅	—	2	2	no	—
108	C₂²×C₄×C₅	—	2	2	no	—
109	C₂²×C₄×C₅	—	2	1	no	—
110	C₂²×C₄×C₅	—	2	1	no	—
111	C₂²×C₄×C₅	—	2	2	no	—
112	C₂²×C₄×C₅	—	2	1	no	—
113	C₂²×C₄×C₅	—	2	1	no	—
114	C₂²×C₄×C₅	—	2	2	no	—
115	C₂²×C₄×C₅	—	4	4	no	—
116	C₂²×C₄×C₅	—	4	4	no	—
117	C₂²×C₄×C₅	—	8	2	no	—
118	C₂²×C₄×C₅	C₂²×C₄	1	4	yes	—
119	C₂²×C₄×C₅	C₂×D₄	1	2	yes	—
120	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
121	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
122	C₂²×C₄×C₅	C₂×Q₈	1	4	yes	—
123	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
124	C₅×M₁₆	—	4	8	no	—
125	C₂×C₅×C₈	—	2	1	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	2	no	—
130	C₂×C₅×C₈	—	2	2	no	—
131	C₂×C₅×C₈	C₂²×C₄	1	2	yes	—
132	C₂×C₅×C₈	C₂²×C₄	1	4	yes	—
133	C₂×C₅×C₈	C₂²×C₄	1	2	yes	—
134	C₅×C₄⋊C₄	—	2	1	no	—
135	C₅×C₄⋊C₄	—	2	1	no	—
136	C₅×C₄⋊C₄	—	2	2	no	—
137	C₅×C₄⋊C₄	—	2	2	no	—
138	C₅×C₄⋊C₄	—	2	1	no	—
139	C₅×C₄⋊C₄	—	2	1	no	—
140	C₅×C₄⋊C₄	—	2	2	no	—
141	C₅×C₄⋊C₄	—	2	2	no	—
142	C₅×C₄⋊C₄	—	2	1	no	—
143	C₅×C₄⋊C₄	—	2	1	no	—
144	C₅×C₄⋊C₄	—	4	4	no	—
145	C₅×C₄⋊C₄	—	4	2	no	—
146	C₅×C₄⋊C₄	—	4	2	no	—
147	C₅×C₄⋊C₄	—	8	1	no	—
148	C₅×C₄⋊C₄	—	8	1	no	—
149	C₅×C₄⋊C₄	C₄⋊C₄	1	4	yes	—
150	C₅×C₄⋊C₄	#41	1	2	yes	—
151	C₅×C₄⋊C₄	#41	1	2	yes	—
152	C₅×C₂²⋊C₄	—	4	4	no	—
153	C₅×C₂²⋊C₄	—	4	4	no	—
154	C₅×C₂²⋊C₄	—	8	2	no	—
155	C₅×C₂²⋊C₄	C₄⋊C₄	1	8	yes	—
156	C₄²×C₅	—	4	4	no	—
157	C₄²×C₅	—	4	2	no	—
158	C₄²×C₅	—	4	2	no	—
159	C₄²×C₅	C₂²×C₄	1	2	yes	—
160	C₄²×C₅	C₂×Q₈	1	2	yes	—
161	C₂²×M₁₆	C₂²×C₅	1	2	yes	—
162	C₂×C₄×D₄	—	2	1	no	—
163	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
164	C₂×#117	C₂²×C₅	1	2	yes	—
165	C₂²×C₄⋊C₄	C₂²×C₅	1	2	yes	—
166	#436	C₄×C₅	1	8	yes	complemented
167	C₂×#107	C₂²×C₅	1	1	yes	characteristic
168	C₂×#107	C₂²×C₅	1	1	yes	characteristic
169	C₂×#107	C₂²×C₅	1	2	yes	—
170	C₂×#106	C₂²×C₅	1	2	yes	—
171	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
172	C₂×C₂²⋊C₈	C₂²×C₅	1	2	yes	—
173	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
174	#390	—	2	1	no	—
175	#389	—	2	1	no	—
176	#388	—	2	2	no	—
177	#385	—	2	2	no	—
178	#384	C₂²×C₅	1	1	yes	characteristic
179	#384	C₂²×C₅	1	1	yes	characteristic
180	#380	C₂²×C₅	1	2	yes	—
181	#380	C₂²×C₅	1	2	yes	—
182	C₄×C₄⋊C₄	—	2	1	no	—
183	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
184	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
185	#340	C₂²×C₅	1	1	yes	characteristic
186	#340	C₂²×C₅	1	2	yes	—
187	#340	C₂²×C₅	1	2	yes	—
188	#340	C₂²×C₅	1	2	yes	—
189	#340	C₂²×C₅	1	2	yes	—
190	#340	C₂²×C₅	1	1	yes	characteristic
191	C₂³×C₅	—	2	2	no	—
192	C₂³×C₅	—	2	2	no	—
193	C₂³×C₅	—	2	2	no	—
194	C₂³×C₅	—	2	2	no	—
195	C₂³×C₅	—	2	2	no	—
196	C₂³×C₅	—	2	2	no	—
197	C₂³×C₅	C₂×C₄⋊C₄	1	4	yes	—
198	C₂³×C₅	C₂²×D₄	1	1	yes	characteristic
199	C₅×D₄	—	2	8	no	—
200	C₂×C₄×C₅	—	2	2	no	—
201	C₂×C₄×C₅	—	2	2	no	—
202	C₂×C₄×C₅	—	2	1	no	—
203	C₂×C₄×C₅	—	2	1	no	—
204	C₂×C₄×C₅	—	2	4	no	—
205	C₂×C₄×C₅	—	2	4	no	—
206	C₂×C₄×C₅	—	2	4	no	—
207	C₂×C₄×C₅	—	2	4	no	—
208	C₂×C₄×C₅	—	2	2	no	—
209	C₂×C₄×C₅	—	2	2	no	—
210	C₂×C₄×C₅	—	4	1	no	—
211	C₂×C₄×C₅	—	4	1	no	—
212	C₂×C₄×C₅	—	4	1	no	—
213	C₂×C₄×C₅	—	4	1	no	—
214	C₂×C₄×C₅	—	4	2	no	—
215	C₂×C₄×C₅	—	4	2	no	—
216	C₂×C₄×C₅	—	4	1	no	—
217	C₂×C₄×C₅	—	4	1	no	—
218	C₂×C₄×C₅	—	4	1	no	—
219	C₂×C₄×C₅	—	4	1	no	—
220	C₂×C₄×C₅	—	4	2	no	—
221	C₂×C₄×C₅	—	4	2	no	—
222	C₂×C₄×C₅	—	4	1	no	—
223	C₂×C₄×C₅	—	4	2	no	—
224	C₂×C₄×C₅	—	4	2	no	—
225	C₂×C₄×C₅	—	4	1	no	—
226	C₂×C₄×C₅	—	8	8	no	—
227	C₂×C₄×C₅	C₂×C₄⋊C₄	1	2	yes	—
228	C₂×C₄×C₅	C₂×C₄⋊C₄	1	4	yes	—
229	C₂×C₄×C₅	C₂×C₄⋊C₄	1	2	yes	—
230	C₂×C₄×C₅	AGL(1,ℤ/8)	1	2	yes	—
231	C₂×C₄×C₅	#137	1	2	yes	—
232	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
233	C₂×C₄×C₅	C₂²×Q₈	1	1	yes	characteristic
234	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
235	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
236	C₂×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
237	C₂×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
238	C₅×C₈	—	2	2	no	—
239	C₅×C₈	—	2	4	no	—
240	C₅×C₈	—	2	2	no	—
241	C₂²×D₄	C₅×D₄	1	1	yes	characteristic
242	C₂³×C₄	—	2	2	no	—
243	C₂³×C₄	C₂³×C₅	1	2	yes	—
244	C₂×M₁₆	—	4	2	no	—
245	C₂×M₁₆	—	4	2	no	—
246	C₂×M₁₆	C₂×C₄×C₅	1	8	yes	complemented
247	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
248	C₂²×C₈	C₂³×C₅	1	2	yes	—
249	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
250	C₄×D₄	—	4	4	no	—
251	C₄×D₄	C₂×C₄×C₅	1	4	yes	—
252	C₄×D₄	C₅×Q₈	1	4	yes	—
253	#117	—	2	4	no	—
254	#117	—	4	2	no	—
255	C₂×C₄⋊C₄	—	2	4	no	—
256	C₂×C₄⋊C₄	—	2	2	no	—
257	C₂×C₄⋊C₄	—	2	1	no	—
258	C₂×C₄⋊C₄	—	2	1	no	—
259	C₂×C₄⋊C₄	—	2	1	no	—
260	C₂×C₄⋊C₄	—	2	1	no	—
261	C₂×C₄⋊C₄	—	4	2	no	—
262	C₂×C₄⋊C₄	C₅×D₄	1	1	yes	characteristic
263	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
264	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
265	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
266	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
267	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
268	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
269	C₂×C₂²⋊C₄	—	2	2	no	—
270	C₂×C₂²⋊C₄	—	2	2	no	—
271	C₂×C₂²⋊C₄	—	2	2	no	—
272	C₂×C₂²⋊C₄	C₅×D₄	1	2	yes	—
273	C₂×C₄²	—	2	2	no	—
274	C₂×C₄²	—	2	1	no	—
275	C₂×C₄²	—	2	1	no	—
276	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
277	#107	—	2	2	no	—
278	#107	—	2	2	no	—
279	#107	—	4	2	no	—
280	#106	—	4	2	no	—
281	C₄⋊C₈	C₂×C₄×C₅	1	4	yes	complemented
282	C₂²⋊C₈	C₂×C₄×C₅	1	8	yes	complemented
283	C₄×C₈	C₂×C₄×C₅	1	4	yes	complemented
284	#95	—	2	2	no	—
285	#95	—	2	1	no	—
286	#95	—	2	1	no	—
287	#95	—	2	2	no	—
288	C₂²×C₅	—	2	4	no	—
289	C₂²×C₅	—	2	4	no	—
290	C₂²×C₅	—	2	4	no	—
291	C₂²×C₅	—	4	2	no	—
292	C₂²×C₅	—	4	2	no	—
293	C₂²×C₅	—	4	2	no	—
294	C₂²×C₅	—	4	2	no	—
295	C₂²×C₅	C₂²×C₄⋊C₄	1	1	yes	characteristic
296	C₂²×C₅	#546	1	1	yes	characteristic
297	C₂²×C₅	#546	1	1	yes	characteristic
298	C₂²×C₅	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
299	C₂²×C₅	C₂×#137	1	1	yes	characteristic
300	C₂²×C₅	#576	1	1	yes	characteristic
301	C₂²×C₅	#578	1	1	yes	characteristic
302	C₄×C₅	—	2	4	no	—
303	C₄×C₅	—	2	2	no	—
304	C₄×C₅	—	4	2	no	—
305	C₄×C₅	—	4	2	no	—
306	C₄×C₅	—	8	1	no	—
307	C₄×C₅	—	8	2	no	—
308	C₄×C₅	—	8	1	no	—
309	C₄×C₅	—	8	2	no	—
310	C₄×C₅	#428	1	4	yes	—
311	C₄×C₅	C₄×#41	1	1	yes	characteristic
312	C₄×C₅	#518	1	1	yes	characteristic
313	C₄×C₅	#554	1	1	yes	characteristic
314	C₄×C₅	#554	1	1	yes	characteristic
315	C₂⁴	C₂×C₅×D₄	1	2	yes	—
316	C₂×D₄	—	2	2	no	—
317	C₂×D₄	—	2	2	no	—
318	C₂×D₄	C₅×C₄⋊C₄	1	4	yes	—
319	C₂²×C₄	—	2	2	no	—
320	C₂²×C₄	—	2	2	no	—
321	C₂²×C₄	—	2	2	no	—
322	C₂²×C₄	—	2	2	no	—
323	C₂²×C₄	—	2	1	no	—
324	C₂²×C₄	—	2	1	no	—
325	C₂²×C₄	—	2	1	no	—
326	C₂²×C₄	—	2	1	no	—
327	C₂²×C₄	—	2	2	no	—
328	C₂²×C₄	—	2	2	no	—
329	C₂²×C₄	—	4	4	no	—
330	C₂²×C₄	—	4	4	no	—
331	C₂²×C₄	—	8	2	no	—
332	C₂²×C₄	C₂²×C₄×C₅	1	4	yes	—
333	C₂²×C₄	C₂×C₅×D₄	1	2	yes	—
334	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
335	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
336	C₂²×C₄	C₂×C₅×Q₈	1	4	yes	—
337	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
338	M₁₆	—	4	8	no	—
339	C₂×C₈	—	2	1	no	—
340	C₂×C₈	—	2	1	no	—
341	C₂×C₈	—	2	2	no	—
342	C₂×C₈	—	2	2	no	—
343	C₂×C₈	—	2	1	no	—
344	C₂×C₈	—	2	1	no	—
345	C₂×C₈	C₂²×C₄×C₅	1	2	yes	—
346	C₂×C₈	C₂²×C₄×C₅	1	2	yes	—
347	C₂×C₈	C₂²×C₄×C₅	1	4	yes	—
348	C₄⋊C₄	—	2	1	no	—
349	C₄⋊C₄	—	2	1	no	—
350	C₄⋊C₄	—	2	1	no	—
351	C₄⋊C₄	—	2	1	no	—
352	C₄⋊C₄	—	2	2	no	—
353	C₄⋊C₄	—	2	2	no	—
354	C₄⋊C₄	—	2	1	no	—
355	C₄⋊C₄	—	2	2	no	—
356	C₄⋊C₄	—	2	1	no	—
357	C₄⋊C₄	—	2	2	no	—
358	C₄⋊C₄	—	4	4	no	—
359	C₄⋊C₄	—	4	2	no	—
360	C₄⋊C₄	—	4	2	no	—
361	C₄⋊C₄	—	8	1	no	—
362	C₄⋊C₄	—	8	1	no	—
363	C₄⋊C₄	C₅×C₄⋊C₄	1	4	yes	—
364	C₄⋊C₄	C₅×#41	1	2	yes	—
365	C₄⋊C₄	C₅×#41	1	2	yes	—
366	C₂²⋊C₄	—	4	4	no	—
367	C₂²⋊C₄	—	4	4	no	—
368	C₂²⋊C₄	—	8	2	no	—
369	C₂²⋊C₄	C₅×C₄⋊C₄	1	8	yes	—
370	C₄²	—	4	4	no	—
371	C₄²	—	4	2	no	—
372	C₄²	—	4	2	no	—
373	C₄²	C₂²×C₄×C₅	1	2	yes	—
374	C₄²	C₂×C₅×Q₈	1	2	yes	—
375	C₂×C₅	—	4	4	no	—
376	C₂×C₅	#2349	1	1	yes	characteristic
377	C₂×C₅	C₂×#428	1	1	yes	characteristic
378	C₂×C₅	#2913	1	1	yes	characteristic
379	C₂×C₅	#3325	1	1	yes	characteristic
380	C₂×C₅	#3328	1	1	yes	characteristic
381	C₂×C₅	#3330	1	1	yes	characteristic
382	C₂×C₅	#3333	1	1	yes	characteristic
383	C₂³	—	2	2	no	—
384	C₂³	—	2	2	no	—
385	C₂³	—	2	2	no	—
386	C₂³	—	2	2	no	—
387	C₂³	—	2	2	no	—
388	C₂³	—	2	2	no	—
389	C₂³	C₂×C₅×C₄⋊C₄	1	4	yes	—
390	C₂³	C₂²×C₅×D₄	1	1	yes	characteristic
391	D₄	—	2	8	no	—
392	C₂×C₄	—	2	2	no	—
393	C₂×C₄	—	2	2	no	—
394	C₂×C₄	—	2	1	no	—
395	C₂×C₄	—	2	1	no	—
396	C₂×C₄	—	2	4	no	—
397	C₂×C₄	—	2	4	no	—
398	C₂×C₄	—	2	4	no	—
399	C₂×C₄	—	2	4	no	—
400	C₂×C₄	—	2	2	no	—
401	C₂×C₄	—	2	2	no	—
402	C₂×C₄	—	4	1	no	—
403	C₂×C₄	—	4	1	no	—
404	C₂×C₄	—	4	1	no	—
405	C₂×C₄	—	4	1	no	—
406	C₂×C₄	—	4	2	no	—
407	C₂×C₄	—	4	2	no	—
408	C₂×C₄	—	4	1	no	—
409	C₂×C₄	—	4	1	no	—
410	C₂×C₄	—	4	1	no	—
411	C₂×C₄	—	4	1	no	—
412	C₂×C₄	—	4	2	no	—
413	C₂×C₄	—	4	2	no	—
414	C₂×C₄	—	4	1	no	—
415	C₂×C₄	—	4	2	no	—
416	C₂×C₄	—	4	2	no	—
417	C₂×C₄	—	4	1	no	—
418	C₂×C₄	—	8	8	no	—
419	C₂×C₄	C₂×C₅×C₄⋊C₄	1	2	yes	—
420	C₂×C₄	C₂×C₅×C₄⋊C₄	1	4	yes	—
421	C₂×C₄	C₂×C₅×C₄⋊C₄	1	2	yes	—
422	C₂×C₄	C₅×AGL(1,ℤ/8)	1	2	yes	—
423	C₂×C₄	C₅×#137	1	2	yes	—
424	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
425	C₂×C₄	C₂²×C₅×Q₈	1	1	yes	characteristic
426	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
427	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
428	C₂×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
429	C₂×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
430	C₈	—	2	2	no	—
431	C₈	—	2	2	no	—
432	C₈	—	2	4	no	—
433	C₅	#22713	1	1	yes	characteristic, direct product factor, Sylow
434	C₂²	—	2	4	no	—
435	C₂²	—	2	4	no	—
436	C₂²	—	2	4	no	—
437	C₂²	—	4	2	no	—
438	C₂²	—	4	2	no	—
439	C₂²	—	4	2	no	—
440	C₂²	—	4	2	no	—
441	C₂²	C₂²×C₅×C₄⋊C₄	1	1	yes	characteristic
442	C₂²	C₅×#546	1	1	yes	characteristic
443	C₂²	C₅×#546	1	1	yes	characteristic
444	C₂²	C₂×C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
445	C₂²	C₂×C₅×#137	1	1	yes	characteristic
446	C₂²	C₅×#576	1	1	yes	characteristic
447	C₂²	C₅×#578	1	1	yes	characteristic
448	C₄	—	2	4	no	—
449	C₄	—	2	2	no	—
450	C₄	—	4	2	no	—
451	C₄	—	4	2	no	—
452	C₄	—	8	2	no	—
453	C₄	—	8	1	no	—
454	C₄	—	8	1	no	—
455	C₄	—	8	2	no	—
456	C₄	C₅×#428	1	4	yes	—
457	C₄	C₄×C₅×#41	1	1	yes	characteristic
458	C₄	C₅×#518	1	1	yes	characteristic
459	C₄	C₅×#554	1	1	yes	characteristic
460	C₄	C₅×#554	1	1	yes	characteristic
461	C₂	—	4	4	no	—
462	C₂	C₅×#2349	1	1	yes	characteristic
463	C₂	C₂×C₅×#428	1	1	yes	characteristic
464	C₂	C₅×#2913	1	1	yes	characteristic
465	C₂	C₅×#3325	1	1	yes	characteristic
466	C₂	C₅×#3328	1	1	yes	characteristic
467	C₂	C₅×#3330	1	1	yes	characteristic
468	C₂	C₅×#3333	1	1	yes	characteristic

	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×D₄	D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₅ ◁ C₂×C₄×C₅×D₄ ◁ G

Complements

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

N	H ≅ G/N	type
4. C₅×#1948	C₂	semidirect
5. C₅×#1947	C₂	semidirect
6. C₅×#1854	C₂	semidirect
7. C₅×#1852	C₂	semidirect
8. C₅×#1834	C₂	semidirect
9. C₅×#1809	C₂	semidirect
10. C₄×C₅×#107	C₂	semidirect
11. C₅×#1736	C₂	semidirect
17. C₅×#436	C₄	semidirect
42. #22713	C₅	direct (N × H)
48. C₂×C₅×M₁₆	C₂×C₄	semidirect
83. C₅×C₄⋊C₈	C₂×C₄	semidirect
84. C₅×C₂²⋊C₈	C₂×C₄	semidirect
85. C₄×C₅×C₈	C₂×C₄	semidirect
93. #1948	C₂×C₅	semidirect
94. #1947	C₂×C₅	semidirect
95. #1854	C₂×C₅	semidirect
96. #1852	C₂×C₅	semidirect
97. #1834	C₂×C₅	semidirect
98. #1809	C₂×C₅	semidirect
99. C₄×#107	C₂×C₅	semidirect
100. #1736	C₂×C₅	semidirect
166. #436	C₄×C₅	semidirect
246. C₂×M₁₆	C₂×C₄×C₅	semidirect
281. C₄⋊C₈	C₂×C₄×C₅	semidirect
282. C₂²⋊C₈	C₂×C₄×C₅	semidirect
283. C₄×C₈	C₂×C₄×C₅	semidirect
433. C₅	#22713	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×#436	2
C₅×#2354	2
C₅×D₄×C₄⋊C₄	2
C₅×#1948	2
C₅×#1947	2
C₅×#1854	2
C₅×#1852	2
C₅×#1834	2
C₅×#1809	2
C₄×C₅×#107	2
C₅×#1736	2
#22713	5

Subgroups — C5×#22713 #11945433

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#22713 #11945433