Subgroups — C₅×#24970 #11947690

Order 1280.

770 conjugacy classes of subgroups.

The subgroup lattice has 476 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×#2354	C₂	1	1	yes	maximal, characteristic
3	C₅×#2075	C₂	1	2	yes	maximal, complemented
4	C₅×#2036	C₂	1	2	yes	maximal, complemented
5	C₅×#1954	C₂	1	1	yes	maximal, characteristic
6	C₅×#1947	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#1873	C₂	1	2	yes	maximal, complemented
8	C₅×#1834	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#1825	C₂	1	2	yes	maximal, complemented
10	C₅×#1803	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×C₅×#103	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₅×C₂²⋊Q₈	C₂²	1	2	yes	—
13	C₂×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
14	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
15	C₂×C₅×#117	C₂²	1	2	yes	—
16	C₂×C₅×#107	C₂²	1	2	yes	—
17	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
18	C₂×C₅×#103	C₂²	1	1	yes	characteristic
19	C₂×C₅×#103	C₂²	1	1	yes	characteristic
20	C₂×C₅×#103	C₂²	1	2	yes	—
21	C₂×C₅×C₂²⋊C₈	C₂²	1	2	yes	—
22	C₂×C₅×C₂²⋊C₈	C₂²	1	2	yes	—
23	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
24	C₅×#396	—	2	2	no	—
25	C₅×#390	—	2	1	no	—
26	C₅×#390	—	2	1	no	—
27	C₅×#389	—	2	1	no	—
28	C₅×#388	—	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	C₅×#340	C₂²	1	1	yes	characteristic
36	C₅×#340	C₂²	1	1	yes	characteristic
37	C₅×#340	C₂²	1	2	yes	—
38	C₅×#340	C₂²	1	2	yes	—
39	C₅×#340	C₂²	1	2	yes	—
40	C₅×#340	C₂²	1	2	yes	—
41	#24970	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
42	C₂²×C₅×Q₈	C₂³	1	1	yes	characteristic
43	C₂²×C₅×D₄	D₄	1	1	yes	characteristic
44	C₂³×C₄×C₅	C₂³	1	2	yes	—
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	—	2	4	no	—
49	C₅×C₂²⋊Q₈	—	4	2	no	—
50	C₄×C₅×Q₈	—	2	2	no	—
51	C₄×C₅×Q₈	—	2	2	no	—
52	C₄×C₅×D₄	—	2	2	no	—
53	C₄×C₅×D₄	—	2	2	no	—
54	C₅×#117	—	2	4	no	—
55	C₅×#117	—	4	2	no	—
56	C₂×C₅×C₄⋊C₄	—	2	1	no	—
57	C₂×C₅×C₄⋊C₄	—	2	1	no	—
58	C₂×C₅×C₄⋊C₄	—	2	2	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	D₄	1	1	yes	characteristic
63	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
64	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
65	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
66	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
67	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
68	C₂×C₅×C₂²⋊C₄	—	2	2	no	—
69	C₂×C₅×C₂²⋊C₄	—	2	2	no	—
70	C₂×C₅×C₂²⋊C₄	—	2	2	no	—
71	C₂×C₅×C₂²⋊C₄	—	2	2	no	—
72	C₂×C₅×C₂²⋊C₄	D₄	1	2	yes	—
73	C₂×C₄²×C₅	—	2	1	no	—
74	C₂×C₄²×C₅	—	2	2	no	—
75	C₂×C₄²×C₅	—	2	1	no	—
76	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
77	C₅×#107	—	4	2	no	—
78	C₅×C₄⋊C₈	—	2	2	no	—
79	C₅×#103	—	2	2	no	—
80	C₅×#103	—	2	2	no	—
81	C₅×#103	—	4	2	no	—
82	C₅×C₂²⋊C₈	—	4	2	no	—
83	C₅×C₂²⋊C₈	—	4	2	no	—
84	C₄×C₅×C₈	—	2	2	no	—
85	C₅×#95	—	2	2	no	—
86	C₅×#95	—	2	1	no	—
87	C₅×#95	—	2	2	no	—
88	#2538	C₂×C₅	1	1	yes	characteristic
89	#2354	C₂×C₅	1	1	yes	characteristic
90	#2075	C₂×C₅	1	2	yes	complemented
91	#2036	C₂×C₅	1	2	yes	complemented
92	#1954	C₂×C₅	1	1	yes	characteristic
93	#1947	C₂×C₅	1	1	yes	characteristic, complemented
94	#1873	C₂×C₅	1	2	yes	complemented
95	#1834	C₂×C₅	1	1	yes	characteristic, complemented
96	#1825	C₂×C₅	1	2	yes	complemented
97	#1803	C₂×C₅	1	1	yes	characteristic, complemented
98	C₄×#103	C₂×C₅	1	1	yes	characteristic, complemented
99	C₂⁴×C₅	C₂×D₄	1	2	yes	—
100	C₂×C₅×Q₈	—	2	1	no	—
101	C₂×C₅×Q₈	—	2	1	no	—
102	C₂×C₅×Q₈	—	2	1	no	—
103	C₂×C₅×Q₈	—	2	1	no	—
104	C₂×C₅×Q₈	—	2	1	no	—
105	C₂×C₅×Q₈	#41	1	2	yes	—
106	C₂×C₅×D₄	—	2	2	no	—
107	C₂×C₅×D₄	—	2	2	no	—
108	C₂×C₅×D₄	—	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	2	no	—
113	C₂²×C₄×C₅	—	2	2	no	—
114	C₂²×C₄×C₅	—	2	2	no	—
115	C₂²×C₄×C₅	—	2	2	no	—
116	C₂²×C₄×C₅	—	2	2	no	—
117	C₂²×C₄×C₅	—	2	2	no	—
118	C₂²×C₄×C₅	—	2	1	no	—
119	C₂²×C₄×C₅	—	2	1	no	—
120	C₂²×C₄×C₅	—	2	2	no	—
121	C₂²×C₄×C₅	C₂×D₄	1	2	yes	—
122	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
123	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
124	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
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	1	no	—
131	C₂×C₅×C₈	—	2	1	no	—
132	C₂×C₅×C₈	—	2	2	no	—
133	C₂×C₅×C₈	—	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	—	2	1	no	—
138	C₅×C₄⋊C₄	—	2	1	no	—
139	C₅×C₄⋊C₄	—	2	2	no	—
140	C₅×C₄⋊C₄	—	2	1	no	—
141	C₅×C₄⋊C₄	—	2	2	no	—
142	C₅×C₄⋊C₄	—	2	2	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	—	4	2	no	—
148	C₅×C₄⋊C₄	—	8	1	no	—
149	C₅×C₄⋊C₄	—	8	1	no	—
150	C₅×C₄⋊C₄	#41	1	2	yes	—
151	C₅×C₂²⋊C₄	—	2	4	no	—
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	—	8	2	no	—
156	C₄²×C₅	—	4	4	no	—
157	C₄²×C₅	—	4	2	no	—
158	C₄²×C₅	—	4	2	no	—
159	C₄²×C₅	#41	1	2	yes	—
160	C₄²×C₅	#41	1	2	yes	—
161	C₂×C₂²⋊Q₈	C₂²×C₅	1	2	yes	—
162	C₂×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
163	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
164	C₂×#117	C₂²×C₅	1	2	yes	—
165	C₂×#107	C₂²×C₅	1	2	yes	—
166	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
167	C₂×#103	C₂²×C₅	1	1	yes	characteristic
168	C₂×#103	C₂²×C₅	1	1	yes	characteristic
169	C₂×#103	C₂²×C₅	1	2	yes	—
170	C₂×C₂²⋊C₈	C₂²×C₅	1	2	yes	—
171	C₂×C₂²⋊C₈	C₂²×C₅	1	2	yes	—
172	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
173	#396	—	2	2	no	—
174	#390	—	2	1	no	—
175	#390	—	2	1	no	—
176	#389	—	2	1	no	—
177	#388	—	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	#340	C₂²×C₅	1	2	yes	—
185	#340	C₂²×C₅	1	1	yes	characteristic
186	#340	C₂²×C₅	1	2	yes	—
187	#340	C₂²×C₅	1	1	yes	characteristic
188	#340	C₂²×C₅	1	2	yes	—
189	#340	C₂²×C₅	1	2	yes	—
190	C₂³×C₅	—	2	2	no	—
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	C₂²×D₄	1	1	yes	characteristic
198	C₅×Q₈	—	2	2	no	—
199	C₅×Q₈	—	2	2	no	—
200	C₅×Q₈	—	4	1	no	—
201	C₅×Q₈	—	4	1	no	—
202	C₅×D₄	—	4	4	no	—
203	C₂×C₄×C₅	—	2	1	no	—
204	C₂×C₄×C₅	—	2	1	no	—
205	C₂×C₄×C₅	—	2	2	no	—
206	C₂×C₄×C₅	—	2	2	no	—
207	C₂×C₄×C₅	—	2	2	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	2	no	—
217	C₂×C₄×C₅	—	4	2	no	—
218	C₂×C₄×C₅	—	4	1	no	—
219	C₂×C₄×C₅	—	4	2	no	—
220	C₂×C₄×C₅	—	4	2	no	—
221	C₂×C₄×C₅	—	4	1	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	2	no	—
228	C₂×C₄×C₅	—	4	2	no	—
229	C₂×C₄×C₅	—	4	1	no	—
230	C₂×C₄×C₅	#123	1	2	yes	—
231	C₂×C₄×C₅	#123	1	2	yes	—
232	C₂×C₄×C₅	#135	1	2	yes	—
233	C₂×C₄×C₅	#137	1	2	yes	—
234	C₂×C₄×C₅	C₂×#41	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	H(5,𝔽₂)	1	1	yes	characteristic
240	C₅×C₈	—	4	2	no	—
241	C₅×C₈	—	4	1	no	—
242	C₅×C₈	—	4	1	no	—
243	C₂²×Q₈	C₂³×C₅	1	1	yes	characteristic
244	C₂²×D₄	C₅×D₄	1	1	yes	characteristic
245	C₂³×C₄	C₂³×C₅	1	2	yes	—
246	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
247	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
248	C₂²×C₈	C₂³×C₅	1	2	yes	—
249	C₂²⋊Q₈	—	2	4	no	—
250	C₂²⋊Q₈	—	4	2	no	—
251	C₄×Q₈	—	2	2	no	—
252	C₄×Q₈	—	2	2	no	—
253	C₄×D₄	—	2	2	no	—
254	C₄×D₄	—	2	2	no	—
255	#117	—	2	4	no	—
256	#117	—	4	2	no	—
257	C₂×C₄⋊C₄	—	2	1	no	—
258	C₂×C₄⋊C₄	—	2	2	no	—
259	C₂×C₄⋊C₄	—	2	1	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	C₅×D₄	1	1	yes	characteristic
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	2	yes	—
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	—	2	2	no	—
273	C₂×C₂²⋊C₄	C₅×D₄	1	2	yes	—
274	C₂×C₄²	—	2	2	no	—
275	C₂×C₄²	—	2	1	no	—
276	C₂×C₄²	—	2	1	no	—
277	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
278	#107	—	4	2	no	—
279	C₄⋊C₈	—	2	2	no	—
280	#103	—	2	2	no	—
281	#103	—	2	2	no	—
282	#103	—	4	2	no	—
283	C₂²⋊C₈	—	4	2	no	—
284	C₂²⋊C₈	—	4	2	no	—
285	C₄×C₈	—	2	2	no	—
286	#95	—	2	2	no	—
287	#95	—	2	1	no	—
288	#95	—	2	2	no	—
289	C₂²×C₅	—	4	2	no	—
290	C₂²×C₅	—	4	2	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	—	4	2	no	—
296	C₂²×C₅	C₂×#123	1	1	yes	characteristic
297	C₂²×C₅	#546	1	1	yes	characteristic
298	C₂²×C₅	#546	1	1	yes	characteristic
299	C₂²×C₅	C₂×#135	1	1	yes	characteristic
300	C₂²×C₅	C₂×#137	1	1	yes	characteristic
301	C₂²×C₅	#576	1	1	yes	characteristic
302	C₂²×C₅	#578	1	1	yes	characteristic
303	C₄×C₅	—	2	2	no	—
304	C₄×C₅	—	4	2	no	—
305	C₄×C₅	—	4	2	no	—
306	C₄×C₅	—	4	2	no	—
307	C₄×C₅	—	8	2	no	—
308	C₄×C₅	—	8	1	no	—
309	C₄×C₅	—	8	2	no	—
310	C₄×C₅	—	8	1	no	—
311	C₄×C₅	#485	1	4	yes	—
312	C₄×C₅	#529	1	1	yes	characteristic
313	C₄×C₅	#540	1	1	yes	characteristic
314	C₄×C₅	#553	1	1	yes	characteristic
315	C₄×C₅	#555	1	1	yes	characteristic
316	C₂⁴	C₂×C₅×D₄	1	2	yes	—
317	C₂×Q₈	—	2	1	no	—
318	C₂×Q₈	—	2	1	no	—
319	C₂×Q₈	—	2	1	no	—
320	C₂×Q₈	—	2	1	no	—
321	C₂×Q₈	—	2	1	no	—
322	C₂×Q₈	C₅×#41	1	2	yes	—
323	C₂×D₄	—	2	2	no	—
324	C₂×D₄	—	2	2	no	—
325	C₂×D₄	—	2	2	no	—
326	C₂²×C₄	—	2	1	no	—
327	C₂²×C₄	—	2	1	no	—
328	C₂²×C₄	—	2	2	no	—
329	C₂²×C₄	—	2	2	no	—
330	C₂²×C₄	—	2	2	no	—
331	C₂²×C₄	—	2	2	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	2	no	—
337	C₂²×C₄	—	2	2	no	—
338	C₂²×C₄	C₂×C₅×D₄	1	2	yes	—
339	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
340	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
341	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
342	C₂×C₈	—	2	1	no	—
343	C₂×C₈	—	2	1	no	—
344	C₂×C₈	—	2	1	no	—
345	C₂×C₈	—	2	1	no	—
346	C₂×C₈	—	2	2	no	—
347	C₂×C₈	—	2	1	no	—
348	C₂×C₈	—	2	1	no	—
349	C₂×C₈	—	2	2	no	—
350	C₂×C₈	—	2	2	no	—
351	C₄⋊C₄	—	2	2	no	—
352	C₄⋊C₄	—	2	1	no	—
353	C₄⋊C₄	—	2	1	no	—
354	C₄⋊C₄	—	2	2	no	—
355	C₄⋊C₄	—	2	1	no	—
356	C₄⋊C₄	—	2	1	no	—
357	C₄⋊C₄	—	2	2	no	—
358	C₄⋊C₄	—	2	2	no	—
359	C₄⋊C₄	—	2	1	no	—
360	C₄⋊C₄	—	2	2	no	—
361	C₄⋊C₄	—	4	4	no	—
362	C₄⋊C₄	—	4	2	no	—
363	C₄⋊C₄	—	4	2	no	—
364	C₄⋊C₄	—	4	2	no	—
365	C₄⋊C₄	—	8	1	no	—
366	C₄⋊C₄	—	8	1	no	—
367	C₄⋊C₄	C₅×#41	1	2	yes	—
368	C₂²⋊C₄	—	2	4	no	—
369	C₂²⋊C₄	—	4	4	no	—
370	C₂²⋊C₄	—	4	4	no	—
371	C₂²⋊C₄	—	8	2	no	—
372	C₂²⋊C₄	—	8	2	no	—
373	C₄²	—	4	4	no	—
374	C₄²	—	4	2	no	—
375	C₄²	—	4	2	no	—
376	C₄²	C₅×#41	1	2	yes	—
377	C₄²	C₅×#41	1	2	yes	—
378	C₂×C₅	—	8	2	no	—
379	C₂×C₅	#2420	1	1	yes	characteristic
380	C₂×C₅	C₂×#485	1	1	yes	characteristic
381	C₂×C₅	#3098	1	1	yes	characteristic
382	C₂×C₅	#3302	1	1	yes	characteristic
383	C₂×C₅	#3305	1	1	yes	characteristic
384	C₂×C₅	#3328	1	1	yes	characteristic
385	C₂×C₅	#3333	1	1	yes	characteristic
386	C₂³	—	2	2	no	—
387	C₂³	—	2	2	no	—
388	C₂³	—	2	2	no	—
389	C₂³	—	2	2	no	—
390	C₂³	—	2	2	no	—
391	C₂³	—	2	2	no	—
392	C₂³	—	2	2	no	—
393	C₂³	C₂²×C₅×D₄	1	1	yes	characteristic
394	Q₈	—	2	2	no	—
395	Q₈	—	2	2	no	—
396	Q₈	—	4	1	no	—
397	Q₈	—	4	1	no	—
398	D₄	—	4	4	no	—
399	C₂×C₄	—	2	1	no	—
400	C₂×C₄	—	2	1	no	—
401	C₂×C₄	—	2	2	no	—
402	C₂×C₄	—	2	2	no	—
403	C₂×C₄	—	2	2	no	—
404	C₂×C₄	—	2	2	no	—
405	C₂×C₄	—	2	2	no	—
406	C₂×C₄	—	4	1	no	—
407	C₂×C₄	—	4	1	no	—
408	C₂×C₄	—	4	1	no	—
409	C₂×C₄	—	4	1	no	—
410	C₂×C₄	—	4	2	no	—
411	C₂×C₄	—	4	2	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	—	4	1	no	—
419	C₂×C₄	—	4	2	no	—
420	C₂×C₄	—	4	2	no	—
421	C₂×C₄	—	4	1	no	—
422	C₂×C₄	—	4	1	no	—
423	C₂×C₄	—	4	2	no	—
424	C₂×C₄	—	4	2	no	—
425	C₂×C₄	—	4	1	no	—
426	C₂×C₄	C₅×#123	1	2	yes	—
427	C₂×C₄	C₅×#123	1	2	yes	—
428	C₂×C₄	C₅×#135	1	2	yes	—
429	C₂×C₄	C₅×#137	1	2	yes	—
430	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
431	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
432	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
433	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
434	C₂×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
435	C₂×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
436	C₈	—	4	2	no	—
437	C₈	—	4	1	no	—
438	C₈	—	4	1	no	—
439	C₅	#24970	1	1	yes	characteristic, direct product factor, Sylow
440	C₂²	—	4	2	no	—
441	C₂²	—	4	2	no	—
442	C₂²	—	4	2	no	—
443	C₂²	—	4	2	no	—
444	C₂²	—	4	2	no	—
445	C₂²	—	4	2	no	—
446	C₂²	—	4	2	no	—
447	C₂²	C₂×C₅×#123	1	1	yes	characteristic
448	C₂²	C₅×#546	1	1	yes	characteristic
449	C₂²	C₅×#546	1	1	yes	characteristic
450	C₂²	C₂×C₅×#135	1	1	yes	characteristic
451	C₂²	C₂×C₅×#137	1	1	yes	characteristic
452	C₂²	C₅×#576	1	1	yes	characteristic
453	C₂²	C₅×#578	1	1	yes	characteristic
454	C₄	—	2	2	no	—
455	C₄	—	4	2	no	—
456	C₄	—	4	2	no	—
457	C₄	—	4	2	no	—
458	C₄	—	8	2	no	—
459	C₄	—	8	1	no	—
460	C₄	—	8	2	no	—
461	C₄	—	8	1	no	—
462	C₄	C₅×#485	1	4	yes	—
463	C₄	C₅×#529	1	1	yes	characteristic
464	C₄	C₅×#540	1	1	yes	characteristic
465	C₄	C₅×#553	1	1	yes	characteristic
466	C₄	C₅×#555	1	1	yes	characteristic
467	C₂	—	8	2	no	—
468	C₂	C₅×#2420	1	1	yes	characteristic
469	C₂	C₂×C₅×#485	1	1	yes	characteristic
470	C₂	C₅×#3098	1	1	yes	characteristic
471	C₂	C₅×#3302	1	1	yes	characteristic
472	C₂	C₅×#3305	1	1	yes	characteristic
473	C₂	C₅×#3328	1	1	yes	characteristic
474	C₂	C₅×#3333	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	D₄
LCS	G ▷ C₂²×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
3. C₅×#2075	C₂	semidirect
4. C₅×#2036	C₂	semidirect
6. C₅×#1947	C₂	semidirect
7. C₅×#1873	C₂	semidirect
8. C₅×#1834	C₂	semidirect
9. C₅×#1825	C₂	semidirect
10. C₅×#1803	C₂	semidirect
11. C₄×C₅×#103	C₂	semidirect
41. #24970	C₅	direct (N × H)
90. #2075	C₂×C₅	semidirect
91. #2036	C₂×C₅	semidirect
93. #1947	C₂×C₅	semidirect
94. #1873	C₂×C₅	semidirect
95. #1834	C₂×C₅	semidirect
96. #1825	C₂×C₅	semidirect
97. #1803	C₂×C₅	semidirect
98. C₄×#103	C₂×C₅	semidirect
439. C₅	#24970	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×#2354	2
C₅×#2075	2
C₅×#2036	2
C₅×#1954	2
C₅×#1947	2
C₅×#1873	2
C₅×#1834	2
C₅×#1825	2
C₅×#1803	2
C₄×C₅×#103	2
#24970	5

Subgroups — C5×#24970 #11947690

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#24970 #11947690