Subgroups — C₅×#21548 #11944268

Order 1280.

914 conjugacy classes of subgroups.

The subgroup lattice has 450 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#3054	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅×#443	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#2929	C₂	1	2	yes	maximal, complemented
4	C₂×C₅×#405	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#1975	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#1946	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#1938	C₂	1	2	yes	maximal, complemented
8	C₅×#1897	C₂	1	2	yes	maximal, complemented
9	C₅×#1811	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#1772	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#1764	C₂	1	2	yes	maximal, complemented
12	C₂×C₅×#135	C₂²	1	1	yes	characteristic
13	C₂×C₅×#131	C₂²	1	2	yes	—
14	C₂²×C₅×M₁₆	C₂²	1	1	yes	characteristic
15	C₂³×C₅×C₈	C₂²	1	1	yes	characteristic
16	C₅×#525	C₂²	1	2	yes	—
17	C₂×C₅×#117	C₂²	1	1	yes	characteristic
18	C₅×#470	C₄	1	2	yes	complemented
19	C₅×#469	C₄	1	2	yes	complemented
20	C₅×#468	C₄	1	4	yes	complemented
21	C₅×#443	—	2	4	no	—
22	C₅×#435	—	2	4	no	—
23	C₅×C₈×D₄	—	2	4	no	—
24	C₂×C₅×#108	C₂²	1	1	yes	characteristic
25	C₂×C₅×#108	C₂²	1	1	yes	characteristic
26	C₅×#427	C₂²	1	1	yes	characteristic
27	C₅×#424	C₂²	1	2	yes	—
28	C₂×C₅×#104	C₂²	1	2	yes	—
29	C₂×C₅×#104	C₂²	1	2	yes	—
30	C₅×#416	C₂²	1	2	yes	—
31	C₅×#408	C₂²	1	2	yes	—
32	C₅×#407	C₂²	1	2	yes	—
33	C₅×#405	—	2	4	no	—
34	C₅×#405	C₂²	1	2	yes	—
35	C₂×C₅×#97	C₂²	1	1	yes	characteristic
36	C₂×C₅×#97	C₂²	1	1	yes	characteristic
37	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
38	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
39	C₅×#341	C₂²	1	2	yes	—
40	C₅×#339	C₂²	1	2	yes	—
41	C₅×#339	C₂²	1	2	yes	—
42	#21548	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
43	C₂×C₅×#41	C₂³	1	2	yes	—
44	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
45	C₅×#135	—	2	2	no	—
46	C₅×#135	—	2	2	no	—
47	C₂×C₅×Q₁₆	C₂×C₄	1	1	yes	characteristic
48	C₂×C₅×SD₁₆	C₂×C₄	1	2	yes	—
49	C₂×C₅×D₈	C₂×C₄	1	1	yes	characteristic
50	C₅×#131	—	2	4	no	—
51	C₅×#131	—	2	4	no	—
52	C₂×C₅×M₁₆	—	2	2	no	—
53	C₂×C₅×M₁₆	—	2	2	no	—
54	C₂×C₅×M₁₆	—	2	2	no	—
55	C₂×C₅×M₁₆	C₂×C₄	1	2	yes	—
56	C₂×C₅×M₁₆	C₂×C₄	1	2	yes	—
57	C₂×C₅×M₁₆	C₂³	1	2	yes	—
58	C₂×C₅×M₁₆	C₂³	1	2	yes	—
59	C₂²×C₅×C₈	—	2	2	no	—
60	C₂²×C₅×C₈	—	2	2	no	—
61	C₂²×C₅×C₈	—	2	2	no	—
62	C₂²×C₅×C₈	D₄	1	2	yes	—
63	C₂²×C₅×C₈	D₄	1	2	yes	—
64	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
65	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
66	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
67	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
68	C₅×#123	—	2	2	no	—
69	C₅×C₂²⋊Q₈	C₂×C₄	1	4	yes	—
70	C₅×#121	C₂×C₄	1	4	yes	—
71	C₅×#120	—	2	2	no	—
72	C₄×C₅×D₄	—	2	4	no	—
73	C₅×#117	—	2	2	no	—
74	C₅×#117	—	2	2	no	—
75	C₅×#117	C₂³	1	2	yes	—
76	C₂×C₅×C₄⋊C₄	—	2	1	no	—
77	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
78	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
79	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
80	C₅×#108	—	2	2	no	—
81	C₅×#108	—	2	2	no	—
82	C₅×#107	C₂×C₄	1	2	yes	—
83	C₅×#106	C₂×C₄	1	2	yes	—
84	C₅×C₄⋊C₈	—	2	4	no	—
85	C₅×#104	—	2	4	no	—
86	C₅×#104	—	2	4	no	—
87	C₅×#103	C₂×C₄	1	4	yes	—
88	C₅×#102	C₂×C₄	1	4	yes	—
89	C₅×C₂²⋊C₈	—	2	4	no	—
90	C₅×C₂²⋊C₈	—	2	4	no	—
91	C₅×#97	—	2	2	no	—
92	C₅×#97	—	2	2	no	—
93	C₅×#97	—	2	2	no	—
94	C₄×C₅×C₈	—	2	2	no	—
95	C₄×C₅×C₈	—	2	2	no	—
96	C₄×C₅×C₈	D₄	1	4	yes	complemented
97	#3054	C₂×C₅	1	1	yes	characteristic
98	C₂×#443	C₂×C₅	1	1	yes	characteristic, complemented
99	#2929	C₂×C₅	1	2	yes	complemented
100	C₂×#405	C₂×C₅	1	1	yes	characteristic, complemented
101	#1975	C₂×C₅	1	1	yes	characteristic, complemented
102	#1946	C₂×C₅	1	1	yes	characteristic, complemented
103	#1938	C₂×C₅	1	2	yes	complemented
104	#1897	C₂×C₅	1	2	yes	complemented
105	#1811	C₂×C₅	1	1	yes	characteristic, complemented
106	#1772	C₂×C₅	1	1	yes	characteristic, complemented
107	#1764	C₂×C₅	1	2	yes	complemented
108	C₂⁴×C₅	#41	1	1	yes	characteristic
109	C₅×#41	—	2	2	no	—
110	C₅×#41	—	2	2	no	—
111	C₅×#41	—	2	2	no	—
112	C₅×#41	—	2	2	no	—
113	C₂×C₅×Q₈	C₂²×C₄	1	2	yes	—
114	C₂×C₅×D₄	—	2	4	no	—
115	C₂×C₅×D₄	—	2	2	no	—
116	C₂×C₅×D₄	C₂²×C₄	1	2	yes	—
117	C₂²×C₄×C₅	—	2	1	no	—
118	C₂²×C₄×C₅	—	2	1	no	—
119	C₂²×C₄×C₅	—	2	1	no	—
120	C₂²×C₄×C₅	—	2	1	no	—
121	C₂²×C₄×C₅	—	2	1	no	—
122	C₂²×C₄×C₅	—	2	1	no	—
123	C₂²×C₄×C₅	—	2	2	no	—
124	C₂²×C₄×C₅	C₂²×C₄	1	2	yes	—
125	C₂²×C₄×C₅	C₂×D₄	1	2	yes	—
126	C₂²×C₄×C₅	#41	1	1	yes	characteristic
127	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
128	C₅×Q₁₆	—	2	2	no	—
129	C₅×SD₁₆	—	2	4	no	—
130	C₅×D₈	—	2	2	no	—
131	C₅×M₁₆	—	2	4	no	—
132	C₅×M₁₆	—	2	4	no	—
133	C₅×M₁₆	—	2	2	no	—
134	C₅×M₁₆	—	2	2	no	—
135	C₅×M₁₆	—	2	2	no	—
136	C₅×M₁₆	—	2	2	no	—
137	C₅×M₁₆	—	4	4	no	—
138	C₂×C₅×C₈	—	2	1	no	—
139	C₂×C₅×C₈	—	2	1	no	—
140	C₂×C₅×C₈	—	2	1	no	—
141	C₂×C₅×C₈	—	2	1	no	—
142	C₂×C₅×C₈	—	2	4	no	—
143	C₂×C₅×C₈	—	2	4	no	—
144	C₂×C₅×C₈	—	2	2	no	—
145	C₂×C₅×C₈	—	2	2	no	—
146	C₂×C₅×C₈	—	4	4	no	—
147	C₂×C₅×C₈	C₂²×C₄	1	2	yes	—
148	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
149	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
150	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
151	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
152	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
153	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
154	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
155	C₂×C₅×C₈	#41	1	2	yes	—
156	C₂×C₅×C₈	#41	1	2	yes	—
157	C₅×C₄⋊C₄	—	2	4	no	—
158	C₅×C₄⋊C₄	—	2	4	no	—
159	C₅×C₄⋊C₄	C₂²×C₄	1	4	yes	—
160	C₅×C₂²⋊C₄	—	2	4	no	—
161	C₅×C₂²⋊C₄	—	2	4	no	—
162	C₅×C₂²⋊C₄	—	2	2	no	—
163	C₅×C₂²⋊C₄	—	2	4	no	—
164	C₄²×C₅	—	2	1	no	—
165	C₄²×C₅	—	2	2	no	—
166	C₄²×C₅	—	2	1	no	—
167	C₄²×C₅	C₂×D₄	1	2	yes	—
168	C₄²×C₅	#41	1	2	yes	—
169	C₂×#135	C₂²×C₅	1	1	yes	characteristic
170	C₂×#131	C₂²×C₅	1	2	yes	—
171	C₂²×M₁₆	C₂²×C₅	1	1	yes	characteristic
172	C₂³×C₈	C₂²×C₅	1	1	yes	characteristic
173	#525	C₂²×C₅	1	2	yes	—
174	C₂×#117	C₂²×C₅	1	1	yes	characteristic
175	#470	C₄×C₅	1	2	yes	complemented
176	#469	C₄×C₅	1	2	yes	complemented
177	#468	C₄×C₅	1	4	yes	complemented
178	#443	—	2	4	no	—
179	#435	—	2	4	no	—
180	C₈×D₄	—	2	4	no	—
181	C₂×#108	C₂²×C₅	1	1	yes	characteristic
182	C₂×#108	C₂²×C₅	1	1	yes	characteristic
183	#427	C₂²×C₅	1	1	yes	characteristic
184	#424	C₂²×C₅	1	2	yes	—
185	C₂×#104	C₂²×C₅	1	2	yes	—
186	C₂×#104	C₂²×C₅	1	2	yes	—
187	#416	C₂²×C₅	1	2	yes	—
188	#408	C₂²×C₅	1	2	yes	—
189	#407	C₂²×C₅	1	2	yes	—
190	#405	—	2	4	no	—
191	#405	C₂²×C₅	1	2	yes	—
192	C₂×#97	C₂²×C₅	1	1	yes	characteristic
193	C₂×#97	C₂²×C₅	1	1	yes	characteristic
194	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
195	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
196	#341	C₂²×C₅	1	2	yes	—
197	#339	C₂²×C₅	1	2	yes	—
198	#339	C₂²×C₅	1	2	yes	—
199	C₂³×C₅	—	2	1	no	—
200	C₂³×C₅	—	2	1	no	—
201	C₂³×C₅	—	2	2	no	—
202	C₂³×C₅	—	4	2	no	—
203	C₂³×C₅	C₄×D₄	1	2	yes	—
204	C₂³×C₅	C₂×#41	1	1	yes	characteristic
205	C₅×Q₈	—	2	2	no	—
206	C₅×Q₈	—	2	2	no	—
207	C₅×D₄	—	2	2	no	—
208	C₅×D₄	—	2	2	no	—
209	C₅×D₄	—	4	8	no	—
210	C₅×D₄	—	4	2	no	—
211	C₅×D₄	—	4	2	no	—
212	C₂×C₄×C₅	—	2	1	no	—
213	C₂×C₄×C₅	—	2	1	no	—
214	C₂×C₄×C₅	—	2	2	no	—
215	C₂×C₄×C₅	—	2	2	no	—
216	C₂×C₄×C₅	—	2	2	no	—
217	C₂×C₄×C₅	—	2	2	no	—
218	C₂×C₄×C₅	—	2	4	no	—
219	C₂×C₄×C₅	—	2	2	no	—
220	C₂×C₄×C₅	—	2	2	no	—
221	C₂×C₄×C₅	—	2	2	no	—
222	C₂×C₄×C₅	—	4	2	no	—
223	C₂×C₄×C₅	—	4	2	no	—
224	C₂×C₄×C₅	—	4	2	no	—
225	C₂×C₄×C₅	—	4	2	no	—
226	C₂×C₄×C₅	C₄×D₄	1	2	yes	—
227	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
228	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
229	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
230	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
231	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
232	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
233	C₅×C₈	—	2	2	no	—
234	C₅×C₈	—	2	2	no	—
235	C₅×C₈	—	4	2	no	—
236	C₅×C₈	—	4	2	no	—
237	C₅×C₈	C₄×D₄	1	2	yes	—
238	C₅×C₈	C₄×D₄	1	2	yes	—
239	C₅×C₈	#121	1	2	yes	—
240	C₅×C₈	#121	1	2	yes	—
241	C₂×#41	C₂³×C₅	1	2	yes	—
242	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
243	#135	—	2	2	no	—
244	#135	—	2	2	no	—
245	C₂×Q₁₆	C₂×C₄×C₅	1	1	yes	characteristic
246	C₂×SD₁₆	C₂×C₄×C₅	1	2	yes	—
247	C₂×D₈	C₂×C₄×C₅	1	1	yes	characteristic
248	#131	—	2	4	no	—
249	#131	—	2	4	no	—
250	C₂×M₁₆	—	2	2	no	—
251	C₂×M₁₆	—	2	2	no	—
252	C₂×M₁₆	—	2	2	no	—
253	C₂×M₁₆	C₂×C₄×C₅	1	2	yes	—
254	C₂×M₁₆	C₂×C₄×C₅	1	2	yes	—
255	C₂×M₁₆	C₂³×C₅	1	2	yes	—
256	C₂×M₁₆	C₂³×C₅	1	2	yes	—
257	C₂²×C₈	—	2	2	no	—
258	C₂²×C₈	—	2	2	no	—
259	C₂²×C₈	—	2	2	no	—
260	C₂²×C₈	C₅×D₄	1	2	yes	—
261	C₂²×C₈	C₅×D₄	1	2	yes	—
262	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
263	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
264	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
265	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
266	#123	—	2	2	no	—
267	C₂²⋊Q₈	C₂×C₄×C₅	1	4	yes	—
268	#121	C₂×C₄×C₅	1	4	yes	—
269	#120	—	2	2	no	—
270	C₄×D₄	—	2	4	no	—
271	#117	—	2	2	no	—
272	#117	—	2	2	no	—
273	#117	C₂³×C₅	1	2	yes	—
274	C₂×C₄⋊C₄	—	2	1	no	—
275	C₂×C₂²⋊C₄	—	2	1	no	—
276	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
277	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
278	#108	—	2	2	no	—
279	#108	—	2	2	no	—
280	#107	C₂×C₄×C₅	1	2	yes	—
281	#106	C₂×C₄×C₅	1	2	yes	—
282	C₄⋊C₈	—	2	4	no	—
283	#104	—	2	4	no	—
284	#104	—	2	4	no	—
285	#103	C₂×C₄×C₅	1	4	yes	—
286	#102	C₂×C₄×C₅	1	4	yes	—
287	C₂²⋊C₈	—	2	4	no	—
288	C₂²⋊C₈	—	2	4	no	—
289	#97	—	2	2	no	—
290	#97	—	2	2	no	—
291	#97	—	2	2	no	—
292	C₄×C₈	—	2	2	no	—
293	C₄×C₈	—	2	2	no	—
294	C₄×C₈	C₅×D₄	1	4	yes	complemented
295	C₂²×C₅	—	2	2	no	—
296	C₂²×C₅	—	2	4	no	—
297	C₂²×C₅	—	2	2	no	—
298	C₂²×C₅	—	4	2	no	—
299	C₂²×C₅	—	4	2	no	—
300	C₂²×C₅	—	4	4	no	—
301	C₂²×C₅	—	4	2	no	—
302	C₂²×C₅	C₂×C₄×D₄	1	1	yes	characteristic
303	C₂²×C₅	#525	1	1	yes	characteristic
304	C₂²×C₅	#529	1	1	yes	characteristic
305	C₄×C₅	—	2	2	no	—
306	C₄×C₅	—	4	2	no	—
307	C₄×C₅	—	4	2	no	—
308	C₄×C₅	—	4	4	no	—
309	C₄×C₅	—	4	2	no	—
310	C₄×C₅	C₂×C₄×D₄	1	1	yes	characteristic
311	C₄×C₅	C₄×#41	1	1	yes	characteristic
312	C₄×C₅	C₂×#121	1	1	yes	characteristic
313	C₄×C₅	#532	1	1	yes	characteristic
314	C₂⁴	C₅×#41	1	1	yes	characteristic
315	#41	—	2	2	no	—
316	#41	—	2	2	no	—
317	#41	—	2	2	no	—
318	#41	—	2	2	no	—
319	C₂×Q₈	C₂²×C₄×C₅	1	2	yes	—
320	C₂×D₄	—	2	4	no	—
321	C₂×D₄	—	2	2	no	—
322	C₂×D₄	C₂²×C₄×C₅	1	2	yes	—
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	1	no	—
328	C₂²×C₄	—	2	1	no	—
329	C₂²×C₄	—	2	2	no	—
330	C₂²×C₄	C₂²×C₄×C₅	1	2	yes	—
331	C₂²×C₄	C₂×C₅×D₄	1	2	yes	—
332	C₂²×C₄	C₅×#41	1	1	yes	characteristic
333	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
334	Q₁₆	—	2	2	no	—
335	SD₁₆	—	2	4	no	—
336	D₈	—	2	2	no	—
337	M₁₆	—	2	4	no	—
338	M₁₆	—	2	4	no	—
339	M₁₆	—	2	2	no	—
340	M₁₆	—	2	2	no	—
341	M₁₆	—	2	2	no	—
342	M₁₆	—	2	2	no	—
343	M₁₆	—	4	4	no	—
344	C₂×C₈	—	2	1	no	—
345	C₂×C₈	—	2	1	no	—
346	C₂×C₈	—	2	1	no	—
347	C₂×C₈	—	2	1	no	—
348	C₂×C₈	—	2	4	no	—
349	C₂×C₈	—	2	4	no	—
350	C₂×C₈	—	2	2	no	—
351	C₂×C₈	—	2	2	no	—
352	C₂×C₈	—	4	4	no	—
353	C₂×C₈	C₂²×C₄×C₅	1	2	yes	—
354	C₂×C₈	C₂²×C₄×C₅	1	1	yes	characteristic
355	C₂×C₈	C₂²×C₄×C₅	1	1	yes	characteristic
356	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
357	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
358	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
359	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
360	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
361	C₂×C₈	C₅×#41	1	2	yes	—
362	C₂×C₈	C₅×#41	1	2	yes	—
363	C₄⋊C₄	—	2	4	no	—
364	C₄⋊C₄	—	2	4	no	—
365	C₄⋊C₄	C₂²×C₄×C₅	1	4	yes	—
366	C₂²⋊C₄	—	2	4	no	—
367	C₂²⋊C₄	—	2	4	no	—
368	C₂²⋊C₄	—	2	2	no	—
369	C₂²⋊C₄	—	2	4	no	—
370	C₄²	—	2	1	no	—
371	C₄²	—	2	2	no	—
372	C₄²	—	2	1	no	—
373	C₄²	C₂×C₅×D₄	1	2	yes	—
374	C₄²	C₅×#41	1	2	yes	—
375	C₂×C₅	—	2	1	no	—
376	C₂×C₅	—	2	1	no	—
377	C₂×C₅	—	4	2	no	—
378	C₂×C₅	—	8	2	no	—
379	C₂×C₅	C₄×#121	1	1	yes	characteristic
380	C₂×C₅	#2955	1	2	yes	—
381	C₂³	—	2	1	no	—
382	C₂³	—	2	1	no	—
383	C₂³	—	2	2	no	—
384	C₂³	—	4	2	no	—
385	C₂³	C₄×C₅×D₄	1	2	yes	—
386	C₂³	C₂×C₅×#41	1	1	yes	characteristic
387	Q₈	—	2	2	no	—
388	Q₈	—	2	2	no	—
389	D₄	—	2	2	no	—
390	D₄	—	2	2	no	—
391	D₄	—	4	8	no	—
392	D₄	—	4	2	no	—
393	D₄	—	4	2	no	—
394	C₂×C₄	—	2	1	no	—
395	C₂×C₄	—	2	1	no	—
396	C₂×C₄	—	2	2	no	—
397	C₂×C₄	—	2	2	no	—
398	C₂×C₄	—	2	2	no	—
399	C₂×C₄	—	2	2	no	—
400	C₂×C₄	—	2	4	no	—
401	C₂×C₄	—	2	2	no	—
402	C₂×C₄	—	2	2	no	—
403	C₂×C₄	—	2	2	no	—
404	C₂×C₄	—	4	2	no	—
405	C₂×C₄	—	4	2	no	—
406	C₂×C₄	—	4	2	no	—
407	C₂×C₄	—	4	2	no	—
408	C₂×C₄	C₄×C₅×D₄	1	2	yes	—
409	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
410	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
411	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
412	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
413	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
414	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
415	C₈	—	2	2	no	—
416	C₈	—	2	2	no	—
417	C₈	—	4	2	no	—
418	C₈	—	4	2	no	—
419	C₈	C₄×C₅×D₄	1	2	yes	—
420	C₈	C₄×C₅×D₄	1	2	yes	—
421	C₈	C₅×#121	1	2	yes	—
422	C₈	C₅×#121	1	2	yes	—
423	C₅	#21548	1	1	yes	characteristic, direct product factor, Sylow
424	C₂²	—	2	2	no	—
425	C₂²	—	2	2	no	—
426	C₂²	—	2	4	no	—
427	C₂²	—	4	2	no	—
428	C₂²	—	4	2	no	—
429	C₂²	—	4	2	no	—
430	C₂²	—	4	4	no	—
431	C₂²	C₂×C₄×C₅×D₄	1	1	yes	characteristic
432	C₂²	C₅×#525	1	1	yes	characteristic
433	C₂²	C₅×#529	1	1	yes	characteristic
434	C₄	—	2	2	no	—
435	C₄	—	4	2	no	—
436	C₄	—	4	2	no	—
437	C₄	—	4	2	no	—
438	C₄	—	4	4	no	—
439	C₄	C₂×C₄×C₅×D₄	1	1	yes	characteristic
440	C₄	C₄×C₅×#41	1	1	yes	characteristic
441	C₄	C₂×C₅×#121	1	1	yes	characteristic
442	C₄	C₅×#532	1	1	yes	characteristic
443	C₂	—	2	1	no	—
444	C₂	—	2	1	no	—
445	C₂	—	4	2	no	—
446	C₂	—	8	2	no	—
447	C₂	C₄×C₅×#121	1	1	yes	characteristic
448	C₂	C₅×#2955	1	2	yes	—

	subgroup	G/H
center	C₂×C₅×C₈	C₂×D₄
commutator	C₂×C₄	C₂³×C₄×C₅
Frattini, cosocle	C₂²×C₄	C₂⁴×C₅
socle	C₂²×C₅	C₂×C₄×D₄
prime radical	C₅×#3054	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₅×C₈ ◁ C₂³×C₅×C₈ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₅×#443	C₂	semidirect
3. C₅×#2929	C₂	semidirect
4. C₂×C₅×#405	C₂	semidirect
5. C₅×#1975	C₂	semidirect
6. C₅×#1946	C₂	semidirect
7. C₅×#1938	C₂	semidirect
8. C₅×#1897	C₂	semidirect
9. C₅×#1811	C₂	semidirect
10. C₅×#1772	C₂	semidirect
11. C₅×#1764	C₂	semidirect
18. C₅×#470	C₄	semidirect
19. C₅×#469	C₄	semidirect
20. C₅×#468	C₄	semidirect
42. #21548	C₅	direct (N × H)
96. C₄×C₅×C₈	D₄	semidirect
98. C₂×#443	C₂×C₅	semidirect
99. #2929	C₂×C₅	semidirect
100. C₂×#405	C₂×C₅	semidirect
101. #1975	C₂×C₅	semidirect
102. #1946	C₂×C₅	semidirect
103. #1938	C₂×C₅	semidirect
104. #1897	C₂×C₅	semidirect
105. #1811	C₂×C₅	semidirect
106. #1772	C₂×C₅	semidirect
107. #1764	C₂×C₅	semidirect
175. #470	C₄×C₅	semidirect
176. #469	C₄×C₅	semidirect
177. #468	C₄×C₅	semidirect
294. C₄×C₈	C₅×D₄	semidirect
423. C₅	#21548	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×#3054	2
C₂×C₅×#443	2
C₅×#2929	2
C₂×C₅×#405	2
C₅×#1975	2
C₅×#1946	2
C₅×#1938	2
C₅×#1897	2
C₅×#1811	2
C₅×#1772	2
C₅×#1764	2
#21548	5

Subgroups — C5×#21548 #11944268

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#21548 #11944268