Subgroups — C₅×#25278 #11947998

Order 1280.

782 conjugacy classes of subgroups.

The subgroup lattice has 458 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#487	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅×#477	C₂	1	1	yes	maximal, characteristic
3	C₅×#2546	C₂	1	1	yes	maximal, characteristic
4	C₅×#2369	C₂	1	1	yes	maximal, characteristic
5	C₅×#2068	C₂	1	2	yes	maximal
6	C₅×#2043	C₂	1	2	yes	maximal
7	C₅×#1981	C₂	1	1	yes	maximal, characteristic
8	C₅×#1981	C₂	1	2	yes	maximal
9	C₅×#1939	C₂	1	1	yes	maximal, characteristic
10	C₅×#1928	C₂	1	2	yes	maximal
11	C₄×C₅×#103	C₂	1	1	yes	maximal, characteristic
12	C₂×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
13	C₂×C₅×C₄⋊Q₈	C₂²	1	2	yes	—
14	C₂×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
15	C₂×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
16	C₅×#487	—	2	4	no	—
17	C₅×#477	—	2	4	no	—
18	C₂×C₅×#107	C₂²	1	2	yes	—
19	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
20	C₂×C₅×C₄⋊C₈	C₂²	1	2	yes	—
21	C₂×C₅×#103	C₂²	1	1	yes	characteristic
22	C₂×C₅×#103	C₂²	1	1	yes	characteristic
23	C₂×C₅×#103	C₂²	1	2	yes	—
24	C₂×C₅×#103	C₂²	1	2	yes	—
25	C₂×C₅×#103	C₂²	1	2	yes	—
26	C₂×C₅×#103	C₂²	1	2	yes	—
27	C₂×C₅×#103	C₂²	1	2	yes	—
28	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
29	C₅×#398	—	2	2	no	—
30	C₅×#391	—	2	2	no	—
31	C₅×#391	C₂²	1	2	yes	—
32	C₅×#389	—	2	1	no	—
33	C₅×#389	—	2	1	no	—
34	C₅×#389	—	2	1	no	—
35	C₅×#389	C₂²	1	2	yes	—
36	C₄×C₅×C₄⋊C₄	—	2	1	no	—
37	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
38	C₄×C₅×C₄⋊C₄	C₂²	1	2	yes	—
39	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
40	C₅×#340	C₂²	1	1	yes	characteristic
41	C₅×#340	C₂²	1	1	yes	characteristic
42	C₅×#336	C₂²	1	2	yes	—
43	#25278	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
44	C₂²×C₅×Q₈	—	2	1	no	—
45	C₂²×C₅×Q₈	C₂³	1	2	yes	—
46	C₂²×C₅×Q₈	C₂³	1	1	yes	characteristic
47	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
48	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
49	C₂²×C₅×C₈	C₂³	1	2	yes	—
50	C₅×C₄⋊Q₈	—	2	4	no	—
51	C₅×C₄⋊Q₈	—	2	2	no	—
52	C₅×C₄⋊Q₈	—	2	2	no	—
53	C₅×C₄⋊Q₈	—	2	2	no	—
54	C₅×C₄⋊Q₈	—	4	2	no	—
55	C₅×C₄⋊Q₈	D₄	1	4	yes	—
56	C₄×C₅×Q₈	—	2	2	no	—
57	C₄×C₅×Q₈	—	2	2	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	2	no	—
62	C₂×C₅×C₄⋊C₄	—	2	1	no	—
63	C₂×C₅×C₄⋊C₄	—	2	1	no	—
64	C₂×C₅×C₄⋊C₄	—	2	2	no	—
65	C₂×C₅×C₄⋊C₄	D₄	1	1	yes	characteristic
66	C₂×C₅×C₄⋊C₄	D₄	1	1	yes	characteristic
67	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
68	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
69	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
70	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
71	C₂×C₄²×C₅	—	2	1	no	—
72	C₂×C₄²×C₅	—	2	1	no	—
73	C₂×C₄²×C₅	—	2	2	no	—
74	C₂×C₄²×C₅	C₂³	1	2	yes	—
75	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
76	C₅×#107	—	2	4	no	—
77	C₅×C₄⋊C₈	—	2	2	no	—
78	C₅×C₄⋊C₈	—	4	2	no	—
79	C₅×#103	—	2	2	no	—
80	C₅×#103	—	2	4	no	—
81	C₅×#103	—	2	4	no	—
82	C₅×#103	—	2	4	no	—
83	C₅×#103	—	2	2	no	—
84	C₅×#103	—	2	4	no	—
85	C₅×#103	—	4	2	no	—
86	C₄×C₅×C₈	—	2	2	no	—
87	C₅×#95	—	2	2	no	—
88	C₅×#95	—	2	2	no	—
89	C₅×#95	—	2	1	no	—
90	C₅×#95	—	2	2	no	—
91	C₅×#95	—	2	2	no	—
92	C₅×#95	D₄	1	2	yes	—
93	C₂×#487	C₂×C₅	1	1	yes	characteristic
94	C₂×#477	C₂×C₅	1	1	yes	characteristic
95	#2546	C₂×C₅	1	1	yes	characteristic
96	#2369	C₂×C₅	1	1	yes	characteristic
97	#2068	C₂×C₅	1	2	yes	—
98	#2043	C₂×C₅	1	2	yes	—
99	#1981	C₂×C₅	1	1	yes	characteristic
100	#1981	C₂×C₅	1	2	yes	—
101	#1939	C₂×C₅	1	1	yes	characteristic
102	#1928	C₂×C₅	1	2	yes	—
103	C₄×#103	C₂×C₅	1	1	yes	characteristic
104	C₂×C₅×Q₈	—	2	4	no	—
105	C₂×C₅×Q₈	—	2	1	no	—
106	C₂×C₅×Q₈	—	2	1	no	—
107	C₂×C₅×Q₈	—	2	2	no	—
108	C₂×C₅×Q₈	—	2	1	no	—
109	C₂×C₅×Q₈	—	2	1	no	—
110	C₂×C₅×Q₈	—	2	2	no	—
111	C₂×C₅×Q₈	—	2	2	no	—
112	C₂×C₅×Q₈	—	2	2	no	—
113	C₂×C₅×Q₈	—	2	2	no	—
114	C₂×C₅×Q₈	—	2	1	no	—
115	C₂×C₅×Q₈	—	2	2	no	—
116	C₂×C₅×Q₈	—	8	1	no	—
117	C₂×C₅×Q₈	—	8	1	no	—
118	C₂×C₅×Q₈	#41	1	2	yes	—
119	C₂²×C₄×C₅	—	2	1	no	—
120	C₂²×C₄×C₅	—	2	1	no	—
121	C₂²×C₄×C₅	—	2	2	no	—
122	C₂²×C₄×C₅	—	2	1	no	—
123	C₂²×C₄×C₅	—	2	1	no	—
124	C₂²×C₄×C₅	—	2	2	no	—
125	C₂²×C₄×C₅	C₂×D₄	1	2	yes	—
126	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
127	C₂²×C₄×C₅	C₂×D₄	1	2	yes	—
128	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
129	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
130	C₂×C₅×C₈	—	2	1	no	—
131	C₂×C₅×C₈	—	2	1	no	—
132	C₂×C₅×C₈	—	2	2	no	—
133	C₂×C₅×C₈	—	2	1	no	—
134	C₂×C₅×C₈	—	2	1	no	—
135	C₂×C₅×C₈	—	2	2	no	—
136	C₂×C₅×C₈	—	2	2	no	—
137	C₂×C₅×C₈	—	2	1	no	—
138	C₂×C₅×C₈	—	2	1	no	—
139	C₅×C₄⋊C₄	—	2	4	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	—	2	1	no	—
145	C₅×C₄⋊C₄	—	2	1	no	—
146	C₅×C₄⋊C₄	—	2	1	no	—
147	C₅×C₄⋊C₄	—	4	4	no	—
148	C₅×C₄⋊C₄	—	4	4	no	—
149	C₅×C₄⋊C₄	—	4	2	no	—
150	C₅×C₄⋊C₄	—	4	2	no	—
151	C₅×C₄⋊C₄	—	4	2	no	—
152	C₅×C₄⋊C₄	—	8	2	no	—
153	C₅×C₄⋊C₄	Q₁₆	1	4	yes	—
154	C₅×C₄⋊C₄	C₂×D₄	1	4	yes	—
155	C₅×C₄⋊C₄	#41	1	2	yes	—
156	C₄²×C₅	—	2	2	no	—
157	C₄²×C₅	—	2	2	no	—
158	C₄²×C₅	—	4	2	no	—
159	C₄²×C₅	—	4	2	no	—
160	C₄²×C₅	—	8	2	no	—
161	C₄²×C₅	C₂×D₄	1	2	yes	—
162	C₄²×C₅	#41	1	2	yes	—
163	C₂×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
164	C₂×C₄⋊Q₈	C₂²×C₅	1	2	yes	—
165	C₂×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
166	C₂×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
167	#487	—	2	4	no	—
168	#477	—	2	4	no	—
169	C₂×#107	C₂²×C₅	1	2	yes	—
170	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
171	C₂×C₄⋊C₈	C₂²×C₅	1	2	yes	—
172	C₂×#103	C₂²×C₅	1	2	yes	—
173	C₂×#103	C₂²×C₅	1	2	yes	—
174	C₂×#103	C₂²×C₅	1	2	yes	—
175	C₂×#103	C₂²×C₅	1	2	yes	—
176	C₂×#103	C₂²×C₅	1	1	yes	characteristic
177	C₂×#103	C₂²×C₅	1	1	yes	characteristic
178	C₂×#103	C₂²×C₅	1	2	yes	—
179	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
180	#398	—	2	2	no	—
181	#391	—	2	2	no	—
182	#391	C₂²×C₅	1	2	yes	—
183	#389	—	2	1	no	—
184	#389	—	2	1	no	—
185	#389	—	2	1	no	—
186	#389	C₂²×C₅	1	2	yes	—
187	C₄×C₄⋊C₄	—	2	1	no	—
188	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	—
189	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
190	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
191	#340	C₂²×C₅	1	1	yes	characteristic
192	#340	C₂²×C₅	1	1	yes	characteristic
193	#336	C₂²×C₅	1	2	yes	—
194	C₂³×C₅	C₂²×D₄	1	1	yes	characteristic
195	C₅×Q₈	—	2	2	no	—
196	C₅×Q₈	—	2	2	no	—
197	C₅×Q₈	—	4	1	no	—
198	C₅×Q₈	—	4	1	no	—
199	C₅×Q₈	—	4	2	no	—
200	C₅×Q₈	—	4	2	no	—
201	C₅×Q₈	—	4	2	no	—
202	C₅×Q₈	—	4	2	no	—
203	C₅×Q₈	—	8	4	no	—
204	C₂×C₄×C₅	—	2	2	no	—
205	C₂×C₄×C₅	—	2	2	no	—
206	C₂×C₄×C₅	—	2	1	no	—
207	C₂×C₄×C₅	—	2	1	no	—
208	C₂×C₄×C₅	—	2	4	no	—
209	C₂×C₄×C₅	—	2	2	no	—
210	C₂×C₄×C₅	—	2	2	no	—
211	C₂×C₄×C₅	—	2	2	no	—
212	C₂×C₄×C₅	—	2	2	no	—
213	C₂×C₄×C₅	—	2	2	no	—
214	C₂×C₄×C₅	—	4	1	no	—
215	C₂×C₄×C₅	—	4	1	no	—
216	C₂×C₄×C₅	—	4	1	no	—
217	C₂×C₄×C₅	—	4	1	no	—
218	C₂×C₄×C₅	—	4	2	no	—
219	C₂×C₄×C₅	—	4	2	no	—
220	C₂×C₄×C₅	—	4	1	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	—	4	1	no	—
227	C₂×C₄×C₅	—	4	1	no	—
228	C₂×C₄×C₅	—	4	1	no	—
229	C₂×C₄×C₅	#121	1	2	yes	—
230	C₂×C₄×C₅	#121	1	2	yes	—
231	C₂×C₄×C₅	C₂×Q₁₆	1	4	yes	—
232	C₂×C₄×C₅	C₂×Q₁₆	1	2	yes	—
233	C₂×C₄×C₅	#137	1	2	yes	—
234	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
235	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
236	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
237	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
238	C₂×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
239	C₂×C₄×C₅	2₋¹⁺⁴	1	1	yes	characteristic
240	C₅×C₈	—	4	1	no	—
241	C₅×C₈	—	4	1	no	—
242	C₅×C₈	—	4	2	no	—
243	C₂²×Q₈	—	2	1	no	—
244	C₂²×Q₈	C₂³×C₅	1	2	yes	—
245	C₂²×Q₈	C₂³×C₅	1	1	yes	characteristic
246	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
247	C₂²×C₈	C₂³×C₅	1	2	yes	—
248	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
249	C₄⋊Q₈	—	2	4	no	—
250	C₄⋊Q₈	—	2	2	no	—
251	C₄⋊Q₈	—	2	2	no	—
252	C₄⋊Q₈	—	2	2	no	—
253	C₄⋊Q₈	—	4	2	no	—
254	C₄⋊Q₈	C₅×D₄	1	4	yes	—
255	C₄×Q₈	—	2	2	no	—
256	C₄×Q₈	—	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	2	no	—
261	C₂×C₄⋊C₄	—	2	2	no	—
262	C₂×C₄⋊C₄	—	2	1	no	—
263	C₂×C₄⋊C₄	—	2	2	no	—
264	C₂×C₄⋊C₄	C₅×D₄	1	1	yes	characteristic
265	C₂×C₄⋊C₄	C₅×D₄	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	2	yes	—
269	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
270	C₂×C₄²	—	2	1	no	—
271	C₂×C₄²	—	2	1	no	—
272	C₂×C₄²	—	2	2	no	—
273	C₂×C₄²	C₂³×C₅	1	2	yes	—
274	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
275	#107	—	2	4	no	—
276	C₄⋊C₈	—	2	2	no	—
277	C₄⋊C₈	—	4	2	no	—
278	#103	—	2	2	no	—
279	#103	—	2	4	no	—
280	#103	—	2	4	no	—
281	#103	—	2	4	no	—
282	#103	—	2	2	no	—
283	#103	—	2	4	no	—
284	#103	—	4	2	no	—
285	C₄×C₈	—	2	2	no	—
286	#95	—	2	2	no	—
287	#95	—	2	2	no	—
288	#95	—	2	1	no	—
289	#95	—	2	2	no	—
290	#95	—	2	2	no	—
291	#95	C₅×D₄	1	2	yes	—
292	C₂²×C₅	C₂×#121	1	1	yes	characteristic
293	C₂²×C₅	#546	1	1	yes	characteristic
294	C₂²×C₅	#548	1	1	yes	characteristic
295	C₂²×C₅	C₂²×Q₁₆	1	1	yes	characteristic
296	C₂²×C₅	C₂×#137	1	1	yes	characteristic
297	C₂²×C₅	#577	1	1	yes	characteristic
298	C₂²×C₅	#577	1	1	yes	characteristic
299	C₄×C₅	—	2	2	no	—
300	C₄×C₅	—	2	4	no	—
301	C₄×C₅	—	4	2	no	—
302	C₄×C₅	—	4	2	no	—
303	C₄×C₅	—	4	2	no	—
304	C₄×C₅	—	4	4	no	—
305	C₄×C₅	—	8	1	no	—
306	C₄×C₅	—	8	2	no	—
307	C₄×C₅	—	8	1	no	—
308	C₄×C₅	#462	1	4	yes	—
309	C₄×C₅	#529	1	1	yes	characteristic
310	C₄×C₅	#542	1	1	yes	characteristic
311	C₄×C₅	#548	1	1	yes	characteristic
312	C₄×C₅	#550	1	1	yes	characteristic
313	C₂×Q₈	—	2	4	no	—
314	C₂×Q₈	—	2	1	no	—
315	C₂×Q₈	—	2	1	no	—
316	C₂×Q₈	—	2	2	no	—
317	C₂×Q₈	—	2	1	no	—
318	C₂×Q₈	—	2	1	no	—
319	C₂×Q₈	—	2	2	no	—
320	C₂×Q₈	—	2	2	no	—
321	C₂×Q₈	—	2	2	no	—
322	C₂×Q₈	—	2	2	no	—
323	C₂×Q₈	—	2	1	no	—
324	C₂×Q₈	—	2	2	no	—
325	C₂×Q₈	—	8	1	no	—
326	C₂×Q₈	—	8	1	no	—
327	C₂×Q₈	C₅×#41	1	2	yes	—
328	C₂²×C₄	—	2	1	no	—
329	C₂²×C₄	—	2	2	no	—
330	C₂²×C₄	—	2	1	no	—
331	C₂²×C₄	—	2	1	no	—
332	C₂²×C₄	—	2	1	no	—
333	C₂²×C₄	—	2	2	no	—
334	C₂²×C₄	C₂×C₅×D₄	1	2	yes	—
335	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
336	C₂²×C₄	C₂×C₅×D₄	1	2	yes	—
337	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
338	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
339	C₂×C₈	—	2	1	no	—
340	C₂×C₈	—	2	1	no	—
341	C₂×C₈	—	2	2	no	—
342	C₂×C₈	—	2	1	no	—
343	C₂×C₈	—	2	2	no	—
344	C₂×C₈	—	2	1	no	—
345	C₂×C₈	—	2	2	no	—
346	C₂×C₈	—	2	1	no	—
347	C₂×C₈	—	2	1	no	—
348	C₄⋊C₄	—	2	4	no	—
349	C₄⋊C₄	—	2	2	no	—
350	C₄⋊C₄	—	2	2	no	—
351	C₄⋊C₄	—	2	1	no	—
352	C₄⋊C₄	—	2	1	no	—
353	C₄⋊C₄	—	2	1	no	—
354	C₄⋊C₄	—	2	1	no	—
355	C₄⋊C₄	—	2	1	no	—
356	C₄⋊C₄	—	4	4	no	—
357	C₄⋊C₄	—	4	4	no	—
358	C₄⋊C₄	—	4	2	no	—
359	C₄⋊C₄	—	4	2	no	—
360	C₄⋊C₄	—	4	2	no	—
361	C₄⋊C₄	—	8	2	no	—
362	C₄⋊C₄	C₅×Q₁₆	1	4	yes	—
363	C₄⋊C₄	C₂×C₅×D₄	1	4	yes	—
364	C₄⋊C₄	C₅×#41	1	2	yes	—
365	C₄²	—	2	2	no	—
366	C₄²	—	2	2	no	—
367	C₄²	—	4	2	no	—
368	C₄²	—	4	2	no	—
369	C₄²	—	8	2	no	—
370	C₄²	C₂×C₅×D₄	1	2	yes	—
371	C₄²	C₅×#41	1	2	yes	—
372	C₂×C₅	#2426	1	1	yes	characteristic
373	C₂×C₅	C₂×#462	1	1	yes	characteristic
374	C₂×C₅	#3042	1	1	yes	characteristic
375	C₂×C₅	#3299	1	1	yes	characteristic
376	C₂×C₅	#3329	1	1	yes	characteristic
377	C₂×C₅	#3363	1	1	yes	characteristic
378	C₂×C₅	#3372	1	1	yes	characteristic
379	C₂³	C₂²×C₅×D₄	1	1	yes	characteristic
380	Q₈	—	2	2	no	—
381	Q₈	—	2	2	no	—
382	Q₈	—	4	1	no	—
383	Q₈	—	4	1	no	—
384	Q₈	—	4	2	no	—
385	Q₈	—	4	2	no	—
386	Q₈	—	4	2	no	—
387	Q₈	—	4	2	no	—
388	Q₈	—	8	4	no	—
389	C₂×C₄	—	2	2	no	—
390	C₂×C₄	—	2	2	no	—
391	C₂×C₄	—	2	1	no	—
392	C₂×C₄	—	2	1	no	—
393	C₂×C₄	—	2	4	no	—
394	C₂×C₄	—	2	2	no	—
395	C₂×C₄	—	2	2	no	—
396	C₂×C₄	—	2	2	no	—
397	C₂×C₄	—	2	2	no	—
398	C₂×C₄	—	2	2	no	—
399	C₂×C₄	—	4	1	no	—
400	C₂×C₄	—	4	1	no	—
401	C₂×C₄	—	4	1	no	—
402	C₂×C₄	—	4	1	no	—
403	C₂×C₄	—	4	2	no	—
404	C₂×C₄	—	4	2	no	—
405	C₂×C₄	—	4	1	no	—
406	C₂×C₄	—	4	2	no	—
407	C₂×C₄	—	4	1	no	—
408	C₂×C₄	—	4	2	no	—
409	C₂×C₄	—	4	2	no	—
410	C₂×C₄	—	4	1	no	—
411	C₂×C₄	—	4	1	no	—
412	C₂×C₄	—	4	1	no	—
413	C₂×C₄	—	4	1	no	—
414	C₂×C₄	C₅×#121	1	2	yes	—
415	C₂×C₄	C₅×#121	1	2	yes	—
416	C₂×C₄	C₂×C₅×Q₁₆	1	4	yes	—
417	C₂×C₄	C₂×C₅×Q₁₆	1	2	yes	—
418	C₂×C₄	C₅×#137	1	2	yes	—
419	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
420	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
421	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
422	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
423	C₂×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
424	C₂×C₄	C₅×2₋¹⁺⁴	1	1	yes	characteristic
425	C₈	—	4	1	no	—
426	C₈	—	4	1	no	—
427	C₈	—	4	2	no	—
428	C₅	#25278	1	1	yes	characteristic, direct product factor, Sylow
429	C₂²	C₂×C₅×#121	1	1	yes	characteristic
430	C₂²	C₅×#546	1	1	yes	characteristic
431	C₂²	C₅×#548	1	1	yes	characteristic
432	C₂²	C₂²×C₅×Q₁₆	1	1	yes	characteristic
433	C₂²	C₂×C₅×#137	1	1	yes	characteristic
434	C₂²	C₅×#577	1	1	yes	characteristic
435	C₂²	C₅×#577	1	1	yes	characteristic
436	C₄	—	2	2	no	—
437	C₄	—	2	4	no	—
438	C₄	—	4	4	no	—
439	C₄	—	4	2	no	—
440	C₄	—	4	2	no	—
441	C₄	—	4	2	no	—
442	C₄	—	8	1	no	—
443	C₄	—	8	1	no	—
444	C₄	—	8	2	no	—
445	C₄	C₅×#462	1	4	yes	—
446	C₄	C₅×#529	1	1	yes	characteristic
447	C₄	C₅×#542	1	1	yes	characteristic
448	C₄	C₅×#548	1	1	yes	characteristic
449	C₄	C₅×#550	1	1	yes	characteristic
450	C₂	C₅×#2426	1	1	yes	characteristic
451	C₂	C₂×C₅×#462	1	1	yes	characteristic
452	C₂	C₅×#3042	1	1	yes	characteristic
453	C₂	C₅×#3299	1	1	yes	characteristic
454	C₂	C₅×#3329	1	1	yes	characteristic
455	C₂	C₅×#3363	1	1	yes	characteristic
456	C₂	C₅×#3372	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
43. #25278	C₅	direct (N × H)
428. C₅	#25278	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×#487	2
C₂×C₅×#477	2
C₅×#2546	2
C₅×#2369	2
C₅×#2068	2
C₅×#2043	2
C₅×#1981	2
C₅×#1939	2
C₅×#1928	2
C₄×C₅×#103	2
#25278	5

Subgroups — C5×#25278 #11947998

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#25278 #11947998