Subgroups — C₅×#24993 #11947713

Order 1280.

706 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#2538	C₂	1	1	yes	maximal, characteristic
2	C₅×#2355	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#2101	C₂	1	2	yes	maximal, complemented
4	C₅×#2073	C₂	1	2	yes	maximal
5	C₅×#1984	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#1947	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#1925	C₂	1	2	yes	maximal
8	C₅×#1921	C₂	1	2	yes	maximal, complemented
9	C₅×#1834	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#1802	C₂	1	1	yes	maximal, characteristic
11	C₄×C₅×#102	C₂	1	1	yes	maximal, characteristic
12	C₂×C₅×C₂²⋊Q₈	—	2	1	no	—
13	C₂×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
14	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
15	C₂×C₅×#107	C₂²	1	2	yes	—
16	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
17	C₂×C₅×#102	C₂²	1	1	yes	characteristic
18	C₂×C₅×#102	C₂²	1	1	yes	characteristic
19	C₂×C₅×#102	C₂²	1	2	yes	—
20	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
21	C₅×#396	—	2	2	no	—
22	C₅×#391	—	2	1	no	—
23	C₅×#390	C₂²	1	2	yes	—
24	C₅×#389	C₂²	1	2	yes	—
25	C₅×#387	—	2	2	no	—
26	C₅×#384	C₂²	1	1	yes	characteristic
27	C₅×#384	C₂²	1	1	yes	characteristic
28	C₅×#382	C₂²	1	2	yes	—
29	C₅×#380	—	2	1	no	—
30	C₄×C₅×C₄⋊C₄	—	2	1	no	—
31	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
32	C₄×C₅×C₄⋊C₄	C₂²	1	2	yes	—
33	C₅×#340	C₂²	1	1	yes	characteristic
34	C₅×#340	C₂²	1	1	yes	characteristic
35	C₅×#340	C₂²	1	2	yes	—
36	C₅×#340	C₂²	1	2	yes	—
37	C₅×#340	C₂²	1	2	yes	—
38	C₅×#340	C₂²	1	2	yes	—
39	C₅×#336	C₂²	1	2	yes	—
40	C₅×#336	C₂²	1	2	yes	—
41	#24993	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
42	C₂²×C₅×Q₈	D₄	1	1	yes	characteristic
43	C₂²×C₅×D₄	C₂³	1	1	yes	characteristic
44	C₂³×C₄×C₅	—	2	1	no	—
45	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
46	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
47	C₂²×C₅×C₈	C₂³	1	2	yes	—
48	C₅×C₂²⋊Q₈	—	4	4	no	—
49	C₄×C₅×Q₈	—	2	2	no	—
50	C₄×C₅×Q₈	—	2	2	no	—
51	C₄×C₅×D₄	—	2	2	no	—
52	C₄×C₅×D₄	—	2	2	no	—
53	C₂×C₅×C₄⋊C₄	—	2	1	no	—
54	C₂×C₅×C₄⋊C₄	—	2	1	no	—
55	C₂×C₅×C₄⋊C₄	—	2	2	no	—
56	C₂×C₅×C₄⋊C₄	—	2	1	no	—
57	C₂×C₅×C₄⋊C₄	—	2	1	no	—
58	C₂×C₅×C₄⋊C₄	D₄	1	1	yes	characteristic
59	C₂×C₅×C₄⋊C₄	D₄	1	2	yes	—
60	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
61	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
62	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
63	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
64	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
65	C₂×C₅×C₂²⋊C₄	—	2	2	no	—
66	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
67	C₂×C₅×C₂²⋊C₄	—	2	2	no	—
68	C₂×C₄²×C₅	—	2	1	no	—
69	C₂×C₄²×C₅	—	2	2	no	—
70	C₂×C₄²×C₅	C₂³	1	2	yes	—
71	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
72	C₅×#107	—	2	4	no	—
73	C₅×C₄⋊C₈	—	2	2	no	—
74	C₅×#102	—	2	2	no	—
75	C₅×#102	—	2	4	no	—
76	C₅×#102	—	2	2	no	—
77	C₄×C₅×C₈	—	2	2	no	—
78	C₅×#95	—	2	2	no	—
79	C₅×#95	—	2	1	no	—
80	C₅×#95	—	2	2	no	—
81	C₅×#95	—	2	2	no	—
82	C₅×#95	—	2	2	no	—
83	#2538	C₂×C₅	1	1	yes	characteristic
84	#2355	C₂×C₅	1	1	yes	characteristic, complemented
85	#2101	C₂×C₅	1	2	yes	complemented
86	#2073	C₂×C₅	1	2	yes	—
87	#1984	C₂×C₅	1	1	yes	characteristic, complemented
88	#1947	C₂×C₅	1	1	yes	characteristic, complemented
89	#1925	C₂×C₅	1	2	yes	—
90	#1921	C₂×C₅	1	2	yes	complemented
91	#1834	C₂×C₅	1	1	yes	characteristic, complemented
92	#1802	C₂×C₅	1	1	yes	characteristic
93	C₄×#102	C₂×C₅	1	1	yes	characteristic
94	C₂⁴×C₅	—	2	1	no	—
95	C₂×C₅×Q₈	—	2	2	no	—
96	C₂×C₅×Q₈	—	2	2	no	—
97	C₂×C₅×Q₈	—	2	2	no	—
98	C₂×C₅×D₄	—	2	1	no	—
99	C₂×C₅×D₄	—	2	1	no	—
100	C₂×C₅×D₄	—	2	1	no	—
101	C₂×C₅×D₄	—	2	1	no	—
102	C₂×C₅×D₄	—	2	1	no	—
103	C₂×C₅×D₄	#41	1	2	yes	—
104	C₂²×C₄×C₅	—	2	1	no	—
105	C₂²×C₄×C₅	—	2	2	no	—
106	C₂²×C₄×C₅	—	2	1	no	—
107	C₂²×C₄×C₅	—	2	2	no	—
108	C₂²×C₄×C₅	—	2	1	no	—
109	C₂²×C₄×C₅	—	4	2	no	—
110	C₂²×C₄×C₅	—	4	2	no	—
111	C₂²×C₄×C₅	—	4	2	no	—
112	C₂²×C₄×C₅	C₂×D₄	1	2	yes	—
113	C₂²×C₄×C₅	C₂×D₄	1	2	yes	—
114	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
115	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
116	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
117	C₂×C₅×C₈	—	2	1	no	—
118	C₂×C₅×C₈	—	2	1	no	—
119	C₂×C₅×C₈	—	2	2	no	—
120	C₂×C₅×C₈	—	2	1	no	—
121	C₂×C₅×C₈	—	2	1	no	—
122	C₂×C₅×C₈	—	2	2	no	—
123	C₂×C₅×C₈	—	2	2	no	—
124	C₂×C₅×C₈	—	2	1	no	—
125	C₂×C₅×C₈	—	2	1	no	—
126	C₅×C₄⋊C₄	—	2	2	no	—
127	C₅×C₄⋊C₄	—	2	4	no	—
128	C₅×C₄⋊C₄	—	2	1	no	—
129	C₅×C₄⋊C₄	—	2	1	no	—
130	C₅×C₄⋊C₄	—	2	1	no	—
131	C₅×C₄⋊C₄	—	2	1	no	—
132	C₅×C₄⋊C₄	—	2	2	no	—
133	C₅×C₄⋊C₄	—	2	2	no	—
134	C₅×C₄⋊C₄	—	2	2	no	—
135	C₅×C₄⋊C₄	—	2	1	no	—
136	C₅×C₄⋊C₄	—	2	2	no	—
137	C₅×C₄⋊C₄	—	4	4	no	—
138	C₅×C₄⋊C₄	—	4	2	no	—
139	C₅×C₄⋊C₄	—	4	2	no	—
140	C₅×C₄⋊C₄	—	8	1	no	—
141	C₅×C₄⋊C₄	—	8	1	no	—
142	C₅×C₄⋊C₄	#41	1	2	yes	—
143	C₅×C₂²⋊C₄	—	4	4	no	—
144	C₅×C₂²⋊C₄	—	4	2	no	—
145	C₅×C₂²⋊C₄	—	8	2	no	—
146	C₄²×C₅	—	2	2	no	—
147	C₄²×C₅	—	2	2	no	—
148	C₄²×C₅	—	4	2	no	—
149	C₄²×C₅	—	8	2	no	—
150	C₄²×C₅	#41	1	2	yes	—
151	C₄²×C₅	#41	1	2	yes	—
152	C₂×C₂²⋊Q₈	—	2	1	no	—
153	C₂×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
154	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
155	C₂×#107	C₂²×C₅	1	2	yes	—
156	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
157	C₂×#102	C₂²×C₅	1	2	yes	—
158	C₂×#102	C₂²×C₅	1	1	yes	characteristic
159	C₂×#102	C₂²×C₅	1	1	yes	characteristic
160	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
161	#396	—	2	2	no	—
162	#391	—	2	1	no	—
163	#390	C₂²×C₅	1	2	yes	—
164	#389	C₂²×C₅	1	2	yes	—
165	#387	—	2	2	no	—
166	#384	C₂²×C₅	1	1	yes	characteristic
167	#384	C₂²×C₅	1	1	yes	characteristic
168	#382	C₂²×C₅	1	2	yes	—
169	#380	—	2	1	no	—
170	C₄×C₄⋊C₄	—	2	1	no	—
171	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	—
172	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
173	#340	C₂²×C₅	1	2	yes	—
174	#340	C₂²×C₅	1	2	yes	—
175	#340	C₂²×C₅	1	2	yes	—
176	#340	C₂²×C₅	1	2	yes	—
177	#340	C₂²×C₅	1	1	yes	characteristic
178	#340	C₂²×C₅	1	1	yes	characteristic
179	#336	C₂²×C₅	1	2	yes	—
180	#336	C₂²×C₅	1	2	yes	—
181	C₂³×C₅	—	2	2	no	—
182	C₂³×C₅	—	4	1	no	—
183	C₂³×C₅	—	4	1	no	—
184	C₂³×C₅	—	4	1	no	—
185	C₂³×C₅	—	4	1	no	—
186	C₂³×C₅	—	4	1	no	—
187	C₂³×C₅	—	4	1	no	—
188	C₂³×C₅	C₂²×D₄	1	1	yes	characteristic
189	C₅×Q₈	—	4	4	no	—
190	C₅×D₄	—	2	2	no	—
191	C₅×D₄	—	2	2	no	—
192	C₅×D₄	—	4	1	no	—
193	C₅×D₄	—	4	1	no	—
194	C₂×C₄×C₅	—	2	1	no	—
195	C₂×C₄×C₅	—	2	1	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	—	2	2	no	—
203	C₂×C₄×C₅	—	4	1	no	—
204	C₂×C₄×C₅	—	4	1	no	—
205	C₂×C₄×C₅	—	4	1	no	—
206	C₂×C₄×C₅	—	4	2	no	—
207	C₂×C₄×C₅	—	4	2	no	—
208	C₂×C₄×C₅	—	4	1	no	—
209	C₂×C₄×C₅	—	4	2	no	—
210	C₂×C₄×C₅	—	4	1	no	—
211	C₂×C₄×C₅	—	4	1	no	—
212	C₂×C₄×C₅	—	4	2	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	—	8	4	no	—
218	C₂×C₄×C₅	#123	1	2	yes	—
219	C₂×C₄×C₅	#123	1	2	yes	—
220	C₂×C₄×C₅	#135	1	2	yes	—
221	C₂×C₄×C₅	AGL(1,ℤ/8)	1	2	yes	—
222	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
223	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
224	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
225	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
226	C₂×C₄×C₅	2₋¹⁺⁴	1	1	yes	characteristic
227	C₂×C₄×C₅	2₋¹⁺⁴	1	1	yes	characteristic
228	C₅×C₈	—	4	2	no	—
229	C₅×C₈	—	4	1	no	—
230	C₅×C₈	—	4	1	no	—
231	C₂²×Q₈	C₅×D₄	1	1	yes	characteristic
232	C₂²×D₄	C₂³×C₅	1	1	yes	characteristic
233	C₂³×C₄	—	2	1	no	—
234	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
235	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
236	C₂²×C₈	C₂³×C₅	1	2	yes	—
237	C₂²⋊Q₈	—	4	4	no	—
238	C₄×Q₈	—	2	2	no	—
239	C₄×Q₈	—	2	2	no	—
240	C₄×D₄	—	2	2	no	—
241	C₄×D₄	—	2	2	no	—
242	C₂×C₄⋊C₄	—	2	1	no	—
243	C₂×C₄⋊C₄	—	2	2	no	—
244	C₂×C₄⋊C₄	—	2	1	no	—
245	C₂×C₄⋊C₄	—	2	1	no	—
246	C₂×C₄⋊C₄	—	2	1	no	—
247	C₂×C₄⋊C₄	C₅×D₄	1	1	yes	characteristic
248	C₂×C₄⋊C₄	C₅×D₄	1	2	yes	—
249	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
250	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
251	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
252	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
253	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
254	C₂×C₂²⋊C₄	—	2	1	no	—
255	C₂×C₂²⋊C₄	—	2	2	no	—
256	C₂×C₂²⋊C₄	—	2	2	no	—
257	C₂×C₄²	—	2	1	no	—
258	C₂×C₄²	—	2	2	no	—
259	C₂×C₄²	C₂³×C₅	1	2	yes	—
260	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
261	#107	—	2	4	no	—
262	C₄⋊C₈	—	2	2	no	—
263	#102	—	2	4	no	—
264	#102	—	2	2	no	—
265	#102	—	2	2	no	—
266	C₄×C₈	—	2	2	no	—
267	#95	—	2	2	no	—
268	#95	—	2	1	no	—
269	#95	—	2	2	no	—
270	#95	—	2	2	no	—
271	#95	—	2	2	no	—
272	C₂²×C₅	—	4	2	no	—
273	C₂²×C₅	—	4	2	no	—
274	C₂²×C₅	—	4	2	no	—
275	C₂²×C₅	—	8	1	no	—
276	C₂²×C₅	—	8	1	no	—
277	C₂²×C₅	—	8	1	no	—
278	C₂²×C₅	—	8	1	no	—
279	C₂²×C₅	C₂×#123	1	1	yes	characteristic
280	C₂²×C₅	#548	1	1	yes	characteristic
281	C₂²×C₅	#548	1	1	yes	characteristic
282	C₂²×C₅	C₂×#135	1	1	yes	characteristic
283	C₂²×C₅	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
284	C₂²×C₅	#576	1	1	yes	characteristic
285	C₂²×C₅	#578	1	1	yes	characteristic
286	C₄×C₅	—	2	2	no	—
287	C₄×C₅	—	4	2	no	—
288	C₄×C₅	—	4	2	no	—
289	C₄×C₅	—	4	2	no	—
290	C₄×C₅	—	8	1	no	—
291	C₄×C₅	—	8	2	no	—
292	C₄×C₅	—	8	2	no	—
293	C₄×C₅	—	8	1	no	—
294	C₄×C₅	#482	1	4	yes	—
295	C₄×C₅	#529	1	1	yes	characteristic
296	C₄×C₅	#541	1	1	yes	characteristic
297	C₄×C₅	#552	1	1	yes	characteristic
298	C₄×C₅	#556	1	1	yes	characteristic
299	C₂⁴	—	2	1	no	—
300	C₂×Q₈	—	2	2	no	—
301	C₂×Q₈	—	2	2	no	—
302	C₂×Q₈	—	2	2	no	—
303	C₂×D₄	—	2	1	no	—
304	C₂×D₄	—	2	1	no	—
305	C₂×D₄	—	2	1	no	—
306	C₂×D₄	—	2	1	no	—
307	C₂×D₄	—	2	1	no	—
308	C₂×D₄	C₅×#41	1	2	yes	—
309	C₂²×C₄	—	2	1	no	—
310	C₂²×C₄	—	2	1	no	—
311	C₂²×C₄	—	2	2	no	—
312	C₂²×C₄	—	2	1	no	—
313	C₂²×C₄	—	2	2	no	—
314	C₂²×C₄	—	4	2	no	—
315	C₂²×C₄	—	4	2	no	—
316	C₂²×C₄	—	4	2	no	—
317	C₂²×C₄	C₂×C₅×D₄	1	2	yes	—
318	C₂²×C₄	C₂×C₅×D₄	1	2	yes	—
319	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
320	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
321	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
322	C₂×C₈	—	2	1	no	—
323	C₂×C₈	—	2	1	no	—
324	C₂×C₈	—	2	2	no	—
325	C₂×C₈	—	2	1	no	—
326	C₂×C₈	—	2	1	no	—
327	C₂×C₈	—	2	2	no	—
328	C₂×C₈	—	2	2	no	—
329	C₂×C₈	—	2	1	no	—
330	C₂×C₈	—	2	1	no	—
331	C₄⋊C₄	—	2	2	no	—
332	C₄⋊C₄	—	2	4	no	—
333	C₄⋊C₄	—	2	1	no	—
334	C₄⋊C₄	—	2	1	no	—
335	C₄⋊C₄	—	2	2	no	—
336	C₄⋊C₄	—	2	2	no	—
337	C₄⋊C₄	—	2	1	no	—
338	C₄⋊C₄	—	2	1	no	—
339	C₄⋊C₄	—	2	2	no	—
340	C₄⋊C₄	—	2	1	no	—
341	C₄⋊C₄	—	2	2	no	—
342	C₄⋊C₄	—	4	4	no	—
343	C₄⋊C₄	—	4	2	no	—
344	C₄⋊C₄	—	4	2	no	—
345	C₄⋊C₄	—	8	1	no	—
346	C₄⋊C₄	—	8	1	no	—
347	C₄⋊C₄	C₅×#41	1	2	yes	—
348	C₂²⋊C₄	—	4	4	no	—
349	C₂²⋊C₄	—	4	2	no	—
350	C₂²⋊C₄	—	8	2	no	—
351	C₄²	—	2	2	no	—
352	C₄²	—	2	2	no	—
353	C₄²	—	4	2	no	—
354	C₄²	—	8	2	no	—
355	C₄²	C₅×#41	1	2	yes	—
356	C₄²	C₅×#41	1	2	yes	—
357	C₂×C₅	—	8	2	no	—
358	C₂×C₅	#2421	1	1	yes	characteristic
359	C₂×C₅	C₂×#482	1	1	yes	characteristic
360	C₂×C₅	#3098	1	1	yes	characteristic
361	C₂×C₅	#3361	1	1	yes	characteristic
362	C₂×C₅	#3364	1	1	yes	characteristic
363	C₂×C₅	#3366	1	1	yes	characteristic
364	C₂×C₅	#3367	1	1	yes	characteristic
365	C₂³	—	2	2	no	—
366	C₂³	—	4	1	no	—
367	C₂³	—	4	1	no	—
368	C₂³	—	4	1	no	—
369	C₂³	—	4	1	no	—
370	C₂³	—	4	1	no	—
371	C₂³	—	4	1	no	—
372	C₂³	C₂²×C₅×D₄	1	1	yes	characteristic
373	Q₈	—	4	4	no	—
374	D₄	—	2	2	no	—
375	D₄	—	2	2	no	—
376	D₄	—	4	1	no	—
377	D₄	—	4	1	no	—
378	C₂×C₄	—	2	1	no	—
379	C₂×C₄	—	2	1	no	—
380	C₂×C₄	—	2	2	no	—
381	C₂×C₄	—	2	2	no	—
382	C₂×C₄	—	2	2	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	—	4	1	no	—
388	C₂×C₄	—	4	1	no	—
389	C₂×C₄	—	4	1	no	—
390	C₂×C₄	—	4	2	no	—
391	C₂×C₄	—	4	2	no	—
392	C₂×C₄	—	4	1	no	—
393	C₂×C₄	—	4	2	no	—
394	C₂×C₄	—	4	1	no	—
395	C₂×C₄	—	4	1	no	—
396	C₂×C₄	—	4	2	no	—
397	C₂×C₄	—	4	1	no	—
398	C₂×C₄	—	4	2	no	—
399	C₂×C₄	—	4	2	no	—
400	C₂×C₄	—	4	1	no	—
401	C₂×C₄	—	8	4	no	—
402	C₂×C₄	C₅×#123	1	2	yes	—
403	C₂×C₄	C₅×#123	1	2	yes	—
404	C₂×C₄	C₅×#135	1	2	yes	—
405	C₂×C₄	C₅×AGL(1,ℤ/8)	1	2	yes	—
406	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
407	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
408	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
409	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
410	C₂×C₄	C₅×2₋¹⁺⁴	1	1	yes	characteristic
411	C₂×C₄	C₅×2₋¹⁺⁴	1	1	yes	characteristic
412	C₈	—	4	2	no	—
413	C₈	—	4	1	no	—
414	C₈	—	4	1	no	—
415	C₅	#24993	1	1	yes	characteristic, direct product factor, Sylow
416	C₂²	—	4	2	no	—
417	C₂²	—	4	2	no	—
418	C₂²	—	4	2	no	—
419	C₂²	—	8	1	no	—
420	C₂²	—	8	1	no	—
421	C₂²	—	8	1	no	—
422	C₂²	—	8	1	no	—
423	C₂²	C₂×C₅×#123	1	1	yes	characteristic
424	C₂²	C₅×#548	1	1	yes	characteristic
425	C₂²	C₅×#548	1	1	yes	characteristic
426	C₂²	C₂×C₅×#135	1	1	yes	characteristic
427	C₂²	C₂×C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
428	C₂²	C₅×#576	1	1	yes	characteristic
429	C₂²	C₅×#578	1	1	yes	characteristic
430	C₄	—	2	2	no	—
431	C₄	—	4	2	no	—
432	C₄	—	4	2	no	—
433	C₄	—	4	2	no	—
434	C₄	—	8	1	no	—
435	C₄	—	8	2	no	—
436	C₄	—	8	2	no	—
437	C₄	—	8	1	no	—
438	C₄	C₅×#482	1	4	yes	—
439	C₄	C₅×#529	1	1	yes	characteristic
440	C₄	C₅×#541	1	1	yes	characteristic
441	C₄	C₅×#552	1	1	yes	characteristic
442	C₄	C₅×#556	1	1	yes	characteristic
443	C₂	—	8	2	no	—
444	C₂	C₅×#2421	1	1	yes	characteristic
445	C₂	C₂×C₅×#482	1	1	yes	characteristic
446	C₂	C₅×#3098	1	1	yes	characteristic
447	C₂	C₅×#3361	1	1	yes	characteristic
448	C₂	C₅×#3364	1	1	yes	characteristic
449	C₂	C₅×#3366	1	1	yes	characteristic
450	C₂	C₅×#3367	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 ◁ C₂×C₄×C₅×Q₈ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₅×#2355	C₂	semidirect
3. C₅×#2101	C₂	semidirect
5. C₅×#1984	C₂	semidirect
6. C₅×#1947	C₂	semidirect
8. C₅×#1921	C₂	semidirect
9. C₅×#1834	C₂	semidirect
41. #24993	C₅	direct (N × H)
84. #2355	C₂×C₅	semidirect
85. #2101	C₂×C₅	semidirect
87. #1984	C₂×C₅	semidirect
88. #1947	C₂×C₅	semidirect
90. #1921	C₂×C₅	semidirect
91. #1834	C₂×C₅	semidirect
415. C₅	#24993	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×#2538	2
C₅×#2355	2
C₅×#2101	2
C₅×#2073	2
C₅×#1984	2
C₅×#1947	2
C₅×#1925	2
C₅×#1921	2
C₅×#1834	2
C₅×#1802	2
C₄×C₅×#102	2
#24993	5

Subgroups — C5×#24993 #11947713

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#24993 #11947713