Subgroups — C₅×#29500 #11952220

Order 1280.

770 conjugacy classes of subgroups.

The subgroup lattice has 478 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#2860	C₂	1	1	yes	maximal, characteristic
2	C₄×C₅×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#2083	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#2071	C₂	1	1	yes	maximal, characteristic
5	C₅×#2043	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#2013	C₂	1	1	yes	maximal, characteristic
7	C₅×#1973	C₂	1	2	yes	maximal
8	C₅×#1935	C₂	1	2	yes	maximal, complemented
9	C₅×#1880	C₂	1	2	yes	maximal
10	C₅×#1863	C₂	1	2	yes	maximal, complemented
11	C₅×#1745	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×C₅×SD₁₆	C₂²	1	2	yes	—
13	C₂×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
14	C₂×C₅×#126	—	2	1	no	—
15	C₂×C₄×C₅×Q₈	C₂²	1	2	yes	—
16	C₂×C₅×#107	C₂²	1	2	yes	—
17	C₂×C₅×#103	C₂²	1	2	yes	—
18	C₂×C₅×#103	C₂²	1	2	yes	—
19	C₂×C₅×#103	C₂²	1	2	yes	—
20	C₂×C₅×#102	C₂²	1	2	yes	—
21	C₂×C₅×#97	C₂²	1	2	yes	—
22	C₅×#391	C₂²	1	2	yes	—
23	C₅×#390	C₂²	1	1	yes	characteristic
24	C₅×#390	C₂²	1	1	yes	characteristic
25	C₅×#390	C₂²	1	1	yes	characteristic
26	C₅×#389	—	2	1	no	—
27	C₅×#389	—	2	1	no	—
28	C₅×#389	C₂²	1	1	yes	characteristic
29	C₅×#389	C₂²	1	1	yes	characteristic
30	C₅×#389	C₂²	1	1	yes	characteristic
31	C₅×#388	—	2	1	no	—
32	C₅×#388	—	2	1	no	—
33	C₅×#388	—	2	1	no	—
34	C₅×#384	C₂²	1	1	yes	characteristic
35	C₄×C₅×C₄⋊C₄	—	2	1	no	—
36	C₄×C₅×C₄⋊C₄	—	2	1	no	—
37	C₄³×C₅	C₂²	1	1	yes	characteristic
38	C₅×#340	C₂²	1	2	yes	—
39	C₅×#340	C₂²	1	2	yes	—
40	C₅×#336	C₂²	1	1	yes	characteristic
41	C₅×#336	C₂²	1	1	yes	characteristic
42	C₅×#336	C₂²	1	2	yes	—
43	#29500	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
44	C₂²×C₅×Q₈	C₂³	1	2	yes	—
45	C₂²×C₅×D₄	C₂³	1	1	yes	characteristic
46	C₂×C₅×SD₁₆	—	2	4	no	—
47	C₂×C₅×SD₁₆	—	2	4	no	—
48	C₂×C₅×SD₁₆	—	4	2	no	—
49	C₂²×C₅×C₈	C₂³	1	2	yes	—
50	C₂²×C₅×C₈	C₂³	1	2	yes	—
51	C₅×C₄⋊Q₈	—	2	4	no	—
52	C₅×#126	—	4	4	no	—
53	C₄×C₅×Q₈	—	4	2	no	—
54	C₄×C₅×Q₈	—	4	2	no	—
55	C₂×C₅×C₄⋊C₄	—	2	1	no	—
56	C₂×C₅×C₄⋊C₄	—	2	1	no	—
57	C₂×C₅×C₄⋊C₄	—	2	1	no	—
58	C₂×C₅×C₄⋊C₄	—	2	1	no	—
59	C₂×C₅×C₄⋊C₄	—	2	1	no	—
60	C₂×C₅×C₄⋊C₄	—	2	1	no	—
61	C₂×C₅×C₄⋊C₄	—	2	1	no	—
62	C₂×C₅×C₄⋊C₄	—	2	2	no	—
63	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
64	C₂×C₅×C₄⋊C₄	C₂³	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×C₂²⋊C₄	—	2	1	no	—
68	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
69	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
70	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
71	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
72	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
73	C₂×C₄²×C₅	—	2	2	no	—
74	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
75	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
76	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
77	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
78	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
79	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
80	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
81	C₅×#107	—	4	2	no	—
82	C₅×#103	—	2	4	no	—
83	C₅×#103	—	2	4	no	—
84	C₅×#103	—	4	2	no	—
85	C₅×#102	—	4	2	no	—
86	C₅×#97	—	2	4	no	—
87	C₅×#95	—	2	2	no	—
88	C₅×#95	—	2	2	no	—
89	C₅×#95	—	2	1	no	—
90	C₅×#95	—	2	1	no	—
91	C₅×#95	—	2	1	no	—
92	#2860	C₂×C₅	1	1	yes	characteristic
93	C₄×C₄⋊Q₈	C₂×C₅	1	1	yes	characteristic, complemented
94	#2083	C₂×C₅	1	1	yes	characteristic, complemented
95	#2071	C₂×C₅	1	1	yes	characteristic
96	#2043	C₂×C₅	1	1	yes	characteristic, complemented
97	#2013	C₂×C₅	1	1	yes	characteristic
98	#1973	C₂×C₅	1	2	yes	—
99	#1935	C₂×C₅	1	2	yes	complemented
100	#1880	C₂×C₅	1	2	yes	—
101	#1863	C₂×C₅	1	2	yes	complemented
102	#1745	C₂×C₅	1	1	yes	characteristic, complemented
103	C₂⁴×C₅	—	2	1	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	—	2	2	no	—
108	C₂×C₅×Q₈	—	2	2	no	—
109	C₂×C₅×Q₈	#41	1	4	yes	—
110	C₂×C₅×D₄	—	2	2	no	—
111	C₂×C₅×D₄	—	2	2	no	—
112	C₂×C₅×D₄	—	2	1	no	—
113	C₂×C₅×D₄	—	2	1	no	—
114	C₂²×C₄×C₅	—	2	2	no	—
115	C₂²×C₄×C₅	—	2	2	no	—
116	C₂²×C₄×C₅	—	2	1	no	—
117	C₂²×C₄×C₅	—	2	1	no	—
118	C₂²×C₄×C₅	—	2	1	no	—
119	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
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×D₄	1	1	yes	characteristic
123	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
124	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
125	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
126	C₅×SD₁₆	—	4	8	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	—	2	2	no	—
132	C₂×C₅×C₈	#41	1	4	yes	—
133	C₅×C₄⋊C₄	—	2	4	no	—
134	C₅×C₄⋊C₄	—	2	4	no	—
135	C₅×C₄⋊C₄	—	2	2	no	—
136	C₅×C₄⋊C₄	—	2	2	no	—
137	C₅×C₄⋊C₄	—	2	2	no	—
138	C₅×C₄⋊C₄	—	2	2	no	—
139	C₅×C₄⋊C₄	—	2	1	no	—
140	C₅×C₄⋊C₄	—	2	1	no	—
141	C₅×C₄⋊C₄	—	4	2	no	—
142	C₅×C₄⋊C₄	—	4	4	no	—
143	C₅×C₄⋊C₄	—	4	2	no	—
144	C₅×C₄⋊C₄	—	4	2	no	—
145	C₅×C₄⋊C₄	—	4	2	no	—
146	C₅×C₄⋊C₄	—	4	2	no	—
147	C₅×C₂²⋊C₄	—	4	2	no	—
148	C₅×C₂²⋊C₄	—	4	2	no	—
149	C₅×C₂²⋊C₄	—	4	2	no	—
150	C₅×C₂²⋊C₄	—	4	2	no	—
151	C₅×C₂²⋊C₄	—	4	2	no	—
152	C₅×C₂²⋊C₄	—	4	2	no	—
153	C₄²×C₅	—	2	2	no	—
154	C₄²×C₅	—	2	2	no	—
155	C₄²×C₅	—	2	2	no	—
156	C₄²×C₅	—	2	2	no	—
157	C₄²×C₅	—	2	2	no	—
158	C₄²×C₅	—	2	1	no	—
159	C₄²×C₅	—	2	1	no	—
160	C₄²×C₅	—	4	1	no	—
161	C₄²×C₅	—	4	4	no	—
162	C₂²×SD₁₆	C₂²×C₅	1	2	yes	—
163	C₂×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
164	C₂×#126	—	2	1	no	—
165	C₂×C₄×Q₈	C₂²×C₅	1	2	yes	—
166	C₂×#107	C₂²×C₅	1	2	yes	—
167	C₂×#103	C₂²×C₅	1	2	yes	—
168	C₂×#103	C₂²×C₅	1	2	yes	—
169	C₂×#103	C₂²×C₅	1	2	yes	—
170	C₂×#102	C₂²×C₅	1	2	yes	—
171	C₂×#97	C₂²×C₅	1	2	yes	—
172	#391	C₂²×C₅	1	2	yes	—
173	#390	C₂²×C₅	1	1	yes	characteristic
174	#390	C₂²×C₅	1	1	yes	characteristic
175	#390	C₂²×C₅	1	1	yes	characteristic
176	#389	—	2	1	no	—
177	#389	—	2	1	no	—
178	#389	C₂²×C₅	1	1	yes	characteristic
179	#389	C₂²×C₅	1	1	yes	characteristic
180	#389	C₂²×C₅	1	1	yes	characteristic
181	#388	—	2	1	no	—
182	#388	—	2	1	no	—
183	#388	—	2	1	no	—
184	#384	C₂²×C₅	1	1	yes	characteristic
185	C₄×C₄⋊C₄	—	2	1	no	—
186	C₄×C₄⋊C₄	—	2	1	no	—
187	C₄³	C₂²×C₅	1	1	yes	characteristic
188	#340	C₂²×C₅	1	2	yes	—
189	#340	C₂²×C₅	1	2	yes	—
190	#336	C₂²×C₅	1	1	yes	characteristic
191	#336	C₂²×C₅	1	1	yes	characteristic
192	#336	C₂²×C₅	1	2	yes	—
193	C₂³×C₅	—	4	1	no	—
194	C₂³×C₅	—	4	1	no	—
195	C₂³×C₅	—	4	1	no	—
196	C₂³×C₅	—	4	1	no	—
197	C₂³×C₅	—	4	1	no	—
198	C₂³×C₅	—	4	1	no	—
199	C₂³×C₅	—	4	1	no	—
200	C₂³×C₅	C₂²×D₄	1	1	yes	characteristic
201	C₅×Q₈	—	2	4	no	—
202	C₅×Q₈	—	2	4	no	—
203	C₅×Q₈	—	4	2	no	—
204	C₅×Q₈	—	4	2	no	—
205	C₅×D₄	—	4	2	no	—
206	C₅×D₄	—	4	2	no	—
207	C₂×C₄×C₅	—	2	1	no	—
208	C₂×C₄×C₅	—	2	1	no	—
209	C₂×C₄×C₅	—	2	1	no	—
210	C₂×C₄×C₅	—	2	1	no	—
211	C₂×C₄×C₅	—	2	1	no	—
212	C₂×C₄×C₅	—	2	1	no	—
213	C₂×C₄×C₅	—	2	4	no	—
214	C₂×C₄×C₅	—	2	1	no	—
215	C₂×C₄×C₅	—	2	1	no	—
216	C₂×C₄×C₅	—	2	1	no	—
217	C₂×C₄×C₅	—	2	1	no	—
218	C₂×C₄×C₅	—	2	1	no	—
219	C₂×C₄×C₅	—	2	1	no	—
220	C₂×C₄×C₅	—	2	1	no	—
221	C₂×C₄×C₅	—	2	1	no	—
222	C₂×C₄×C₅	—	2	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	—	4	1	no	—
227	C₂×C₄×C₅	—	4	2	no	—
228	C₂×C₄×C₅	—	4	1	no	—
229	C₂×C₄×C₅	—	4	1	no	—
230	C₂×C₄×C₅	—	4	1	no	—
231	C₂×C₄×C₅	—	4	1	no	—
232	C₂×C₄×C₅	—	4	2	no	—
233	C₂×C₄×C₅	—	4	1	no	—
234	C₂×C₄×C₅	—	4	1	no	—
235	C₂×C₄×C₅	—	4	1	no	—
236	C₂×C₄×C₅	—	4	2	no	—
237	C₂×C₄×C₅	AGL(1,ℤ/8)	1	2	yes	—
238	C₂×C₄×C₅	#137	1	2	yes	—
239	C₂×C₄×C₅	#137	1	2	yes	—
240	C₂×C₄×C₅	C₂×#41	1	2	yes	—
241	C₂×C₄×C₅	C₂×#41	1	2	yes	—
242	C₂×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
243	C₂×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
244	C₅×C₈	—	2	4	no	—
245	C₅×C₈	—	4	2	no	—
246	C₂²×Q₈	C₂³×C₅	1	2	yes	—
247	C₂²×D₄	C₂³×C₅	1	1	yes	characteristic
248	C₂×SD₁₆	—	2	4	no	—
249	C₂×SD₁₆	—	2	4	no	—
250	C₂×SD₁₆	—	4	2	no	—
251	C₂²×C₈	C₂³×C₅	1	2	yes	—
252	C₂²×C₈	C₂³×C₅	1	2	yes	—
253	C₄⋊Q₈	—	2	4	no	—
254	#126	—	4	4	no	—
255	C₄×Q₈	—	4	2	no	—
256	C₄×Q₈	—	4	2	no	—
257	C₂×C₄⋊C₄	—	2	1	no	—
258	C₂×C₄⋊C₄	—	2	1	no	—
259	C₂×C₄⋊C₄	—	2	2	no	—
260	C₂×C₄⋊C₄	—	2	1	no	—
261	C₂×C₄⋊C₄	—	2	1	no	—
262	C₂×C₄⋊C₄	—	2	1	no	—
263	C₂×C₄⋊C₄	—	2	1	no	—
264	C₂×C₄⋊C₄	—	2	1	no	—
265	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
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	1	no	—
270	C₂×C₂²⋊C₄	—	2	1	no	—
271	C₂×C₂²⋊C₄	—	2	1	no	—
272	C₂×C₂²⋊C₄	—	2	1	no	—
273	C₂×C₂²⋊C₄	—	2	1	no	—
274	C₂×C₂²⋊C₄	—	2	1	no	—
275	C₂×C₄²	—	2	2	no	—
276	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
277	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
278	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
279	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
280	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
281	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
282	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
283	#107	—	4	2	no	—
284	#103	—	2	4	no	—
285	#103	—	2	4	no	—
286	#103	—	4	2	no	—
287	#102	—	4	2	no	—
288	#97	—	2	4	no	—
289	#95	—	2	2	no	—
290	#95	—	2	2	no	—
291	#95	—	2	1	no	—
292	#95	—	2	1	no	—
293	#95	—	2	1	no	—
294	C₂²×C₅	—	8	1	no	—
295	C₂²×C₅	—	8	1	no	—
296	C₂²×C₅	—	8	1	no	—
297	C₂²×C₅	—	8	1	no	—
298	C₂²×C₅	—	8	1	no	—
299	C₂²×C₅	—	8	1	no	—
300	C₂²×C₅	—	8	1	no	—
301	C₂²×C₅	#525	1	1	yes	characteristic
302	C₂²×C₅	#532	1	1	yes	characteristic
303	C₂²×C₅	#535	1	1	yes	characteristic
304	C₂²×C₅	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
305	C₂²×C₅	C₂×#137	1	1	yes	characteristic
306	C₂²×C₅	C₂×#137	1	1	yes	characteristic
307	C₂²×C₅	#575	1	1	yes	characteristic
308	C₄×C₅	—	2	2	no	—
309	C₄×C₅	—	2	2	no	—
310	C₄×C₅	—	2	2	no	—
311	C₄×C₅	—	4	4	no	—
312	C₄×C₅	—	4	1	no	—
313	C₄×C₅	—	4	1	no	—
314	C₄×C₅	—	4	1	no	—
315	C₄×C₅	—	8	1	no	—
316	C₄×C₅	—	8	1	no	—
317	C₄×C₅	—	8	2	no	—
318	C₄×C₅	—	8	1	no	—
319	C₄×C₅	#551	1	2	yes	—
320	C₄×C₅	#553	1	2	yes	—
321	C₂⁴	—	2	1	no	—
322	C₂×Q₈	—	2	2	no	—
323	C₂×Q₈	—	2	2	no	—
324	C₂×Q₈	—	2	2	no	—
325	C₂×Q₈	—	2	2	no	—
326	C₂×Q₈	—	2	2	no	—
327	C₂×Q₈	C₅×#41	1	4	yes	—
328	C₂×D₄	—	2	2	no	—
329	C₂×D₄	—	2	2	no	—
330	C₂×D₄	—	2	1	no	—
331	C₂×D₄	—	2	1	no	—
332	C₂²×C₄	—	2	2	no	—
333	C₂²×C₄	—	2	2	no	—
334	C₂²×C₄	—	2	1	no	—
335	C₂²×C₄	—	2	1	no	—
336	C₂²×C₄	—	2	1	no	—
337	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
338	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
339	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
340	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
341	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
342	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
343	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
344	SD₁₆	—	4	8	no	—
345	C₂×C₈	—	2	2	no	—
346	C₂×C₈	—	2	2	no	—
347	C₂×C₈	—	2	2	no	—
348	C₂×C₈	—	2	2	no	—
349	C₂×C₈	—	2	2	no	—
350	C₂×C₈	C₅×#41	1	4	yes	—
351	C₄⋊C₄	—	2	4	no	—
352	C₄⋊C₄	—	2	4	no	—
353	C₄⋊C₄	—	2	2	no	—
354	C₄⋊C₄	—	2	2	no	—
355	C₄⋊C₄	—	2	2	no	—
356	C₄⋊C₄	—	2	1	no	—
357	C₄⋊C₄	—	2	1	no	—
358	C₄⋊C₄	—	2	2	no	—
359	C₄⋊C₄	—	4	4	no	—
360	C₄⋊C₄	—	4	2	no	—
361	C₄⋊C₄	—	4	2	no	—
362	C₄⋊C₄	—	4	2	no	—
363	C₄⋊C₄	—	4	2	no	—
364	C₄⋊C₄	—	4	2	no	—
365	C₂²⋊C₄	—	4	2	no	—
366	C₂²⋊C₄	—	4	2	no	—
367	C₂²⋊C₄	—	4	2	no	—
368	C₂²⋊C₄	—	4	2	no	—
369	C₂²⋊C₄	—	4	2	no	—
370	C₂²⋊C₄	—	4	2	no	—
371	C₄²	—	2	2	no	—
372	C₄²	—	2	2	no	—
373	C₄²	—	2	2	no	—
374	C₄²	—	2	2	no	—
375	C₄²	—	2	2	no	—
376	C₄²	—	2	1	no	—
377	C₄²	—	2	1	no	—
378	C₄²	—	4	1	no	—
379	C₄²	—	4	4	no	—
380	C₂×C₅	—	16	1	no	—
381	C₂×C₅	#2603	1	1	yes	characteristic
382	C₂×C₅	#3112	1	1	yes	characteristic
383	C₂×C₅	#3117	1	1	yes	characteristic
384	C₂×C₅	#3172	1	1	yes	characteristic
385	C₂×C₅	#3182	1	1	yes	characteristic
386	C₂×C₅	#3214	1	1	yes	characteristic
387	C₂×C₅	#3218	1	1	yes	characteristic
388	C₂³	—	4	1	no	—
389	C₂³	—	4	1	no	—
390	C₂³	—	4	1	no	—
391	C₂³	—	4	1	no	—
392	C₂³	—	4	1	no	—
393	C₂³	—	4	1	no	—
394	C₂³	—	4	1	no	—
395	C₂³	C₂²×C₅×D₄	1	1	yes	characteristic
396	Q₈	—	2	4	no	—
397	Q₈	—	2	4	no	—
398	Q₈	—	4	2	no	—
399	Q₈	—	4	2	no	—
400	D₄	—	4	2	no	—
401	D₄	—	4	2	no	—
402	C₂×C₄	—	2	1	no	—
403	C₂×C₄	—	2	1	no	—
404	C₂×C₄	—	2	1	no	—
405	C₂×C₄	—	2	1	no	—
406	C₂×C₄	—	2	1	no	—
407	C₂×C₄	—	2	1	no	—
408	C₂×C₄	—	2	4	no	—
409	C₂×C₄	—	2	1	no	—
410	C₂×C₄	—	2	1	no	—
411	C₂×C₄	—	2	1	no	—
412	C₂×C₄	—	2	1	no	—
413	C₂×C₄	—	2	1	no	—
414	C₂×C₄	—	2	1	no	—
415	C₂×C₄	—	2	1	no	—
416	C₂×C₄	—	2	1	no	—
417	C₂×C₄	—	2	1	no	—
418	C₂×C₄	—	4	2	no	—
419	C₂×C₄	—	4	2	no	—
420	C₂×C₄	—	4	1	no	—
421	C₂×C₄	—	4	1	no	—
422	C₂×C₄	—	4	2	no	—
423	C₂×C₄	—	4	1	no	—
424	C₂×C₄	—	4	1	no	—
425	C₂×C₄	—	4	1	no	—
426	C₂×C₄	—	4	1	no	—
427	C₂×C₄	—	4	2	no	—
428	C₂×C₄	—	4	1	no	—
429	C₂×C₄	—	4	1	no	—
430	C₂×C₄	—	4	1	no	—
431	C₂×C₄	—	4	2	no	—
432	C₂×C₄	C₅×AGL(1,ℤ/8)	1	2	yes	—
433	C₂×C₄	C₅×#137	1	2	yes	—
434	C₂×C₄	C₅×#137	1	2	yes	—
435	C₂×C₄	C₂×C₅×#41	1	2	yes	—
436	C₂×C₄	C₂×C₅×#41	1	2	yes	—
437	C₂×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
438	C₂×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
439	C₈	—	2	4	no	—
440	C₈	—	4	2	no	—
441	C₅	#29500	1	1	yes	characteristic, direct product factor, Sylow
442	C₂²	—	8	1	no	—
443	C₂²	—	8	1	no	—
444	C₂²	—	8	1	no	—
445	C₂²	—	8	1	no	—
446	C₂²	—	8	1	no	—
447	C₂²	—	8	1	no	—
448	C₂²	—	8	1	no	—
449	C₂²	C₅×#525	1	1	yes	characteristic
450	C₂²	C₅×#532	1	1	yes	characteristic
451	C₂²	C₅×#535	1	1	yes	characteristic
452	C₂²	C₂×C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
453	C₂²	C₂×C₅×#137	1	1	yes	characteristic
454	C₂²	C₂×C₅×#137	1	1	yes	characteristic
455	C₂²	C₅×#575	1	1	yes	characteristic
456	C₄	—	2	2	no	—
457	C₄	—	2	2	no	—
458	C₄	—	2	2	no	—
459	C₄	—	4	4	no	—
460	C₄	—	4	1	no	—
461	C₄	—	4	1	no	—
462	C₄	—	4	1	no	—
463	C₄	—	8	1	no	—
464	C₄	—	8	1	no	—
465	C₄	—	8	2	no	—
466	C₄	—	8	1	no	—
467	C₄	C₅×#551	1	2	yes	—
468	C₄	C₅×#553	1	2	yes	—
469	C₂	—	16	1	no	—
470	C₂	C₅×#2603	1	1	yes	characteristic
471	C₂	C₅×#3112	1	1	yes	characteristic
472	C₂	C₅×#3117	1	1	yes	characteristic
473	C₂	C₅×#3172	1	1	yes	characteristic
474	C₂	C₅×#3182	1	1	yes	characteristic
475	C₂	C₅×#3214	1	1	yes	characteristic
476	C₂	C₅×#3218	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₅	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₅
prime radical	C₂²×C₅×D₄	C₂³
LCS	G ▷ C₂²×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
2. C₄×C₅×C₄⋊Q₈	C₂	semidirect
3. C₅×#2083	C₂	semidirect
5. C₅×#2043	C₂	semidirect
8. C₅×#1935	C₂	semidirect
10. C₅×#1863	C₂	semidirect
11. C₅×#1745	C₂	semidirect
43. #29500	C₅	direct (N × H)
93. C₄×C₄⋊Q₈	C₂×C₅	semidirect
94. #2083	C₂×C₅	semidirect
96. #2043	C₂×C₅	semidirect
99. #1935	C₂×C₅	semidirect
101. #1863	C₂×C₅	semidirect
102. #1745	C₂×C₅	semidirect
441. C₅	#29500	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×#2860	2
C₄×C₅×C₄⋊Q₈	2
C₅×#2083	2
C₅×#2071	2
C₅×#2043	2
C₅×#2013	2
C₅×#1973	2
C₅×#1935	2
C₅×#1880	2
C₅×#1863	2
C₅×#1745	2
#29500	5

Subgroups — C5×#29500 #11952220

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#29500 #11952220