Subgroups — C₅×#24344 #11947064

Order 1280.

988 conjugacy classes of subgroups.

The subgroup lattice has 462 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#557	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅×#477	C₂	1	1	yes	maximal, characteristic
3	C₂×C₅×#441	C₂	1	1	yes	maximal, characteristic
4	C₅×#2581	C₂	1	1	yes	maximal, characteristic
5	C₅×#2059	C₂	1	2	yes	maximal
6	C₅×#2026	C₂	1	2	yes	maximal
7	C₅×#1993	C₂	1	1	yes	maximal, characteristic
8	C₅×#1985	C₂	1	1	yes	maximal, characteristic
9	C₅×#1878	C₂	1	2	yes	maximal
10	C₅×#1863	C₂	1	2	yes	maximal
11	C₅×#1805	C₂	1	1	yes	maximal, characteristic
12	C₂²×C₅×Q₁₆	C₂²	1	1	yes	characteristic
13	C₅×#557	—	2	4	no	—
14	C₅×#557	—	2	4	no	—
15	C₂×C₅×C₄⋊Q₈	—	2	1	no	—
16	C₂×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
17	C₂×C₅×#125	—	2	2	no	—
18	C₂×C₅×#125	C₂²	1	2	yes	—
19	C₂×C₄×C₅×Q₈	—	2	1	no	—
20	C₂×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
21	C₂×C₄×C₅×Q₈	C₂²	1	2	yes	—
22	C₂×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
23	C₂×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
24	C₅×#477	—	2	4	no	—
25	C₅×#441	—	2	4	no	—
26	C₂×C₅×#107	C₂²	1	2	yes	—
27	C₂×C₅×#106	C₂²	1	1	yes	characteristic
28	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
29	C₂×C₅×#103	C₂²	1	1	yes	characteristic
30	C₂×C₅×#103	C₂²	1	2	yes	—
31	C₂×C₅×#103	C₂²	1	2	yes	—
32	C₂×C₅×#103	C₂²	1	1	yes	characteristic
33	C₂×C₅×#97	C₂²	1	1	yes	characteristic
34	C₅×#400	—	2	1	no	—
35	C₅×#395	—	2	1	no	—
36	C₅×#391	C₂²	1	2	yes	—
37	C₅×#389	C₂²	1	2	yes	—
38	C₅×#387	—	2	2	no	—
39	C₅×#382	C₂²	1	1	yes	characteristic
40	C₅×#340	C₂²	1	2	yes	—
41	C₅×#340	C₂²	1	2	yes	—
42	C₅×#340	C₂²	1	2	yes	—
43	C₅×#336	C₂²	1	2	yes	—
44	C₅×#336	C₂²	1	2	yes	—
45	#24344	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
46	C₂²×C₅×Q₈	—	2	1	no	—
47	C₂²×C₅×Q₈	D₄	1	1	yes	characteristic
48	C₂²×C₅×Q₈	C₂³	1	1	yes	characteristic
49	C₂²×C₅×Q₈	C₂³	1	1	yes	characteristic
50	C₂×C₅×Q₁₆	—	2	2	no	—
51	C₂×C₅×Q₁₆	—	2	2	no	—
52	C₂×C₅×Q₁₆	Q₈	1	4	yes	complemented
53	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
54	C₂²×C₅×C₈	C₂³	1	2	yes	—
55	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
56	C₅×C₄⋊Q₈	—	2	8	no	—
57	C₅×C₄⋊Q₈	—	2	2	no	—
58	C₅×C₄⋊Q₈	D₄	1	4	yes	—
59	C₅×#125	—	2	16	no	—
60	C₅×#125	—	2	4	no	—
61	C₅×#125	—	2	4	no	—
62	C₄×C₅×Q₈	—	2	8	no	—
63	C₄×C₅×Q₈	—	2	4	no	—
64	C₄×C₅×Q₈	—	2	4	no	—
65	C₄×C₅×Q₈	—	2	2	no	—
66	C₄×C₅×Q₈	—	2	2	no	—
67	C₄×C₅×Q₈	—	2	2	no	—
68	C₄×C₅×Q₈	—	2	2	no	—
69	C₄×C₅×Q₈	—	2	2	no	—
70	C₄×C₅×Q₈	D₄	1	4	yes	—
71	C₂×C₅×C₄⋊C₄	—	2	2	no	—
72	C₂×C₅×C₄⋊C₄	—	2	1	no	—
73	C₂×C₅×C₄⋊C₄	—	2	2	no	—
74	C₂×C₅×C₄⋊C₄	—	2	1	no	—
75	C₂×C₅×C₄⋊C₄	—	2	2	no	—
76	C₂×C₅×C₄⋊C₄	—	2	2	no	—
77	C₂×C₅×C₄⋊C₄	—	2	1	no	—
78	C₂×C₅×C₄⋊C₄	D₄	1	2	yes	—
79	C₂×C₅×C₄⋊C₄	D₄	1	1	yes	characteristic
80	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
81	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
82	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
83	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
84	C₂×C₄²×C₅	—	2	2	no	—
85	C₂×C₄²×C₅	—	2	1	no	—
86	C₂×C₄²×C₅	—	2	1	no	—
87	C₂×C₄²×C₅	C₂³	1	2	yes	—
88	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
89	C₅×#107	—	2	4	no	—
90	C₅×#106	—	2	2	no	—
91	C₅×C₄⋊C₈	—	2	2	no	—
92	C₅×#103	—	2	2	no	—
93	C₅×#103	—	2	4	no	—
94	C₅×#103	—	2	2	no	—
95	C₅×#103	—	2	4	no	—
96	C₅×#97	—	2	2	no	—
97	C₅×#95	—	2	1	no	—
98	C₅×#95	—	2	1	no	—
99	C₅×#95	—	2	2	no	—
100	C₅×#95	—	2	2	no	—
101	C₅×#95	—	2	2	no	—
102	C₂×#557	C₂×C₅	1	1	yes	characteristic
103	C₂×#477	C₂×C₅	1	1	yes	characteristic
104	C₂×#441	C₂×C₅	1	1	yes	characteristic
105	#2581	C₂×C₅	1	1	yes	characteristic
106	#2059	C₂×C₅	1	2	yes	—
107	#2026	C₂×C₅	1	2	yes	—
108	#1993	C₂×C₅	1	1	yes	characteristic
109	#1985	C₂×C₅	1	1	yes	characteristic
110	#1878	C₂×C₅	1	2	yes	—
111	#1863	C₂×C₅	1	2	yes	—
112	#1805	C₂×C₅	1	1	yes	characteristic
113	C₂×C₅×Q₈	—	2	2	no	—
114	C₂×C₅×Q₈	—	2	4	no	—
115	C₂×C₅×Q₈	—	2	1	no	—
116	C₂×C₅×Q₈	—	2	1	no	—
117	C₂×C₅×Q₈	—	2	1	no	—
118	C₂×C₅×Q₈	—	2	1	no	—
119	C₂×C₅×Q₈	—	2	1	no	—
120	C₂×C₅×Q₈	—	2	1	no	—
121	C₂×C₅×Q₈	—	2	1	no	—
122	C₂×C₅×Q₈	—	2	1	no	—
123	C₂×C₅×Q₈	—	4	2	no	—
124	C₂×C₅×Q₈	—	4	4	no	—
125	C₂×C₅×Q₈	C₂×D₄	1	2	yes	—
126	C₂×C₅×Q₈	C₂×Q₈	1	2	yes	—
127	C₂×C₅×Q₈	C₂×Q₈	1	2	yes	—
128	C₂×C₅×Q₈	#41	1	2	yes	—
129	C₂²×C₄×C₅	—	2	1	no	—
130	C₂²×C₄×C₅	—	2	1	no	—
131	C₂²×C₄×C₅	—	2	2	no	—
132	C₂²×C₄×C₅	—	2	1	no	—
133	C₂²×C₄×C₅	—	2	1	no	—
134	C₂²×C₄×C₅	—	2	2	no	—
135	C₂²×C₄×C₅	C₂×D₄	1	2	yes	—
136	C₂²×C₄×C₅	C₂×D₄	1	2	yes	—
137	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
138	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
139	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
140	C₅×Q₁₆	—	2	8	no	—
141	C₂×C₅×C₈	—	2	1	no	—
142	C₂×C₅×C₈	—	2	1	no	—
143	C₂×C₅×C₈	—	2	1	no	—
144	C₂×C₅×C₈	—	2	2	no	—
145	C₂×C₅×C₈	—	2	2	no	—
146	C₂×C₅×C₈	—	2	1	no	—
147	C₂×C₅×C₈	—	2	1	no	—
148	C₂×C₅×C₈	—	2	2	no	—
149	C₂×C₅×C₈	C₂×Q₈	1	2	yes	—
150	C₅×C₄⋊C₄	—	2	8	no	—
151	C₅×C₄⋊C₄	—	2	8	no	—
152	C₅×C₄⋊C₄	—	2	8	no	—
153	C₅×C₄⋊C₄	—	2	4	no	—
154	C₅×C₄⋊C₄	—	2	4	no	—
155	C₅×C₄⋊C₄	—	2	2	no	—
156	C₅×C₄⋊C₄	—	2	4	no	—
157	C₅×C₄⋊C₄	—	2	1	no	—
158	C₅×C₄⋊C₄	—	2	2	no	—
159	C₅×C₄⋊C₄	—	2	1	no	—
160	C₅×C₄⋊C₄	—	2	1	no	—
161	C₅×C₄⋊C₄	—	2	2	no	—
162	C₅×C₄⋊C₄	—	2	2	no	—
163	C₅×C₄⋊C₄	—	4	4	no	—
164	C₅×C₄⋊C₄	—	4	2	no	—
165	C₅×C₄⋊C₄	C₂×D₄	1	4	yes	—
166	C₅×C₄⋊C₄	C₂×D₄	1	2	yes	—
167	C₄²×C₅	—	2	8	no	—
168	C₄²×C₅	—	2	4	no	—
169	C₄²×C₅	—	2	2	no	—
170	C₄²×C₅	—	2	2	no	—
171	C₄²×C₅	—	4	2	no	—
172	C₄²×C₅	C₂×D₄	1	2	yes	—
173	C₄²×C₅	C₂×D₄	1	2	yes	—
174	C₂²×Q₁₆	C₂²×C₅	1	1	yes	characteristic
175	#557	—	2	4	no	—
176	#557	—	2	4	no	—
177	C₂×C₄⋊Q₈	—	2	1	no	—
178	C₂×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
179	C₂×#125	—	2	2	no	—
180	C₂×#125	C₂²×C₅	1	2	yes	—
181	C₂×C₄×Q₈	—	2	1	no	—
182	C₂×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
183	C₂×C₄×Q₈	C₂²×C₅	1	2	yes	—
184	C₂×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
185	C₂×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
186	#477	—	2	4	no	—
187	#441	—	2	4	no	—
188	C₂×#107	C₂²×C₅	1	2	yes	—
189	C₂×#106	C₂²×C₅	1	1	yes	characteristic
190	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
191	C₂×#103	C₂²×C₅	1	2	yes	—
192	C₂×#103	C₂²×C₅	1	2	yes	—
193	C₂×#103	C₂²×C₅	1	1	yes	characteristic
194	C₂×#103	C₂²×C₅	1	1	yes	characteristic
195	C₂×#97	C₂²×C₅	1	1	yes	characteristic
196	#400	—	2	1	no	—
197	#395	—	2	1	no	—
198	#391	C₂²×C₅	1	2	yes	—
199	#389	C₂²×C₅	1	2	yes	—
200	#387	—	2	2	no	—
201	#382	C₂²×C₅	1	1	yes	characteristic
202	#340	C₂²×C₅	1	2	yes	—
203	#340	C₂²×C₅	1	2	yes	—
204	#340	C₂²×C₅	1	2	yes	—
205	#336	C₂²×C₅	1	2	yes	—
206	#336	C₂²×C₅	1	2	yes	—
207	C₂³×C₅	C₂²×D₄	1	1	yes	characteristic
208	C₅×Q₈	—	2	2	no	—
209	C₅×Q₈	—	2	2	no	—
210	C₅×Q₈	—	2	2	no	—
211	C₅×Q₈	—	2	2	no	—
212	C₅×Q₈	—	2	2	no	—
213	C₅×Q₈	—	4	4	no	—
214	C₅×Q₈	—	4	8	no	—
215	C₅×Q₈	—	4	1	no	—
216	C₅×Q₈	—	4	1	no	—
217	C₅×Q₈	C₂²⋊Q₈	1	4	yes	—
218	C₂×C₄×C₅	—	2	2	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	—	2	2	no	—
223	C₂×C₄×C₅	—	2	2	no	—
224	C₂×C₄×C₅	—	2	2	no	—
225	C₂×C₄×C₅	—	2	2	no	—
226	C₂×C₄×C₅	—	2	4	no	—
227	C₂×C₄×C₅	—	2	2	no	—
228	C₂×C₄×C₅	—	2	2	no	—
229	C₂×C₄×C₅	—	2	2	no	—
230	C₂×C₄×C₅	—	2	4	no	—
231	C₂×C₄×C₅	—	4	1	no	—
232	C₂×C₄×C₅	—	4	1	no	—
233	C₂×C₄×C₅	—	4	4	no	—
234	C₂×C₄×C₅	—	4	2	no	—
235	C₂×C₄×C₅	—	4	1	no	—
236	C₂×C₄×C₅	—	4	2	no	—
237	C₂×C₄×C₅	—	4	2	no	—
238	C₂×C₄×C₅	—	4	2	no	—
239	C₂×C₄×C₅	—	4	2	no	—
240	C₂×C₄×C₅	#120	1	2	yes	—
241	C₂×C₄×C₅	#120	1	2	yes	—
242	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
243	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
244	C₂×C₄×C₅	C₂²×Q₈	1	1	yes	characteristic
245	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
246	C₂×C₄×C₅	2₋¹⁺⁴	1	1	yes	characteristic
247	C₂×C₄×C₅	2₋¹⁺⁴	1	1	yes	characteristic
248	C₅×C₈	—	2	2	no	—
249	C₅×C₈	—	4	1	no	—
250	C₅×C₈	—	4	2	no	—
251	C₂²×Q₈	—	2	1	no	—
252	C₂²×Q₈	C₅×D₄	1	1	yes	characteristic
253	C₂²×Q₈	C₂³×C₅	1	1	yes	characteristic
254	C₂²×Q₈	C₂³×C₅	1	1	yes	characteristic
255	C₂×Q₁₆	—	2	2	no	—
256	C₂×Q₁₆	—	2	2	no	—
257	C₂×Q₁₆	C₅×Q₈	1	4	yes	complemented
258	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
259	C₂²×C₈	C₂³×C₅	1	2	yes	—
260	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
261	C₄⋊Q₈	—	2	8	no	—
262	C₄⋊Q₈	—	2	2	no	—
263	C₄⋊Q₈	C₅×D₄	1	4	yes	—
264	#125	—	2	16	no	—
265	#125	—	2	4	no	—
266	#125	—	2	4	no	—
267	C₄×Q₈	—	2	8	no	—
268	C₄×Q₈	—	2	4	no	—
269	C₄×Q₈	—	2	4	no	—
270	C₄×Q₈	—	2	2	no	—
271	C₄×Q₈	—	2	2	no	—
272	C₄×Q₈	—	2	2	no	—
273	C₄×Q₈	—	2	2	no	—
274	C₄×Q₈	—	2	2	no	—
275	C₄×Q₈	C₅×D₄	1	4	yes	—
276	C₂×C₄⋊C₄	—	2	2	no	—
277	C₂×C₄⋊C₄	—	2	1	no	—
278	C₂×C₄⋊C₄	—	2	2	no	—
279	C₂×C₄⋊C₄	—	2	1	no	—
280	C₂×C₄⋊C₄	—	2	2	no	—
281	C₂×C₄⋊C₄	—	2	1	no	—
282	C₂×C₄⋊C₄	—	2	2	no	—
283	C₂×C₄⋊C₄	C₅×D₄	1	1	yes	characteristic
284	C₂×C₄⋊C₄	C₅×D₄	1	2	yes	—
285	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
286	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
287	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
288	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
289	C₂×C₄²	—	2	2	no	—
290	C₂×C₄²	—	2	1	no	—
291	C₂×C₄²	—	2	1	no	—
292	C₂×C₄²	C₂³×C₅	1	2	yes	—
293	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
294	#107	—	2	4	no	—
295	#106	—	2	2	no	—
296	C₄⋊C₈	—	2	2	no	—
297	#103	—	2	2	no	—
298	#103	—	2	4	no	—
299	#103	—	2	2	no	—
300	#103	—	2	4	no	—
301	#97	—	2	2	no	—
302	#95	—	2	1	no	—
303	#95	—	2	1	no	—
304	#95	—	2	2	no	—
305	#95	—	2	2	no	—
306	#95	—	2	2	no	—
307	C₂²×C₅	C₂×#120	1	1	yes	characteristic
308	C₂²×C₅	#548	1	1	yes	characteristic
309	C₂²×C₅	D₄×Q₈	1	1	yes	characteristic
310	C₂²×C₅	#575	1	2	yes	—
311	C₂²×C₅	#578	1	2	yes	—
312	C₄×C₅	—	2	4	no	—
313	C₄×C₅	—	2	2	no	—
314	C₄×C₅	—	2	2	no	—
315	C₄×C₅	—	4	2	no	—
316	C₄×C₅	—	4	2	no	—
317	C₄×C₅	—	4	4	no	—
318	C₄×C₅	—	4	2	no	—
319	C₄×C₅	—	4	2	no	—
320	C₄×C₅	—	8	2	no	—
321	C₄×C₅	—	8	1	no	—
322	C₄×C₅	C₂×C₂²⋊Q₈	1	1	yes	characteristic
323	C₄×C₅	#536	1	1	yes	characteristic
324	C₄×C₅	#548	1	1	yes	characteristic
325	C₄×C₅	D₄×Q₈	1	1	yes	characteristic
326	C₂×Q₈	—	2	2	no	—
327	C₂×Q₈	—	2	4	no	—
328	C₂×Q₈	—	2	1	no	—
329	C₂×Q₈	—	2	1	no	—
330	C₂×Q₈	—	2	1	no	—
331	C₂×Q₈	—	2	1	no	—
332	C₂×Q₈	—	2	1	no	—
333	C₂×Q₈	—	2	1	no	—
334	C₂×Q₈	—	2	1	no	—
335	C₂×Q₈	—	2	1	no	—
336	C₂×Q₈	—	4	2	no	—
337	C₂×Q₈	—	4	4	no	—
338	C₂×Q₈	C₂×C₅×D₄	1	2	yes	—
339	C₂×Q₈	C₂×C₅×Q₈	1	2	yes	—
340	C₂×Q₈	C₂×C₅×Q₈	1	2	yes	—
341	C₂×Q₈	C₅×#41	1	2	yes	—
342	C₂²×C₄	—	2	1	no	—
343	C₂²×C₄	—	2	1	no	—
344	C₂²×C₄	—	2	1	no	—
345	C₂²×C₄	—	2	2	no	—
346	C₂²×C₄	—	2	2	no	—
347	C₂²×C₄	—	2	1	no	—
348	C₂²×C₄	C₂×C₅×D₄	1	2	yes	—
349	C₂²×C₄	C₂×C₅×D₄	1	2	yes	—
350	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
351	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
352	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
353	Q₁₆	—	2	8	no	—
354	C₂×C₈	—	2	1	no	—
355	C₂×C₈	—	2	1	no	—
356	C₂×C₈	—	2	1	no	—
357	C₂×C₈	—	2	2	no	—
358	C₂×C₈	—	2	2	no	—
359	C₂×C₈	—	2	1	no	—
360	C₂×C₈	—	2	1	no	—
361	C₂×C₈	—	2	2	no	—
362	C₂×C₈	C₂×C₅×Q₈	1	2	yes	—
363	C₄⋊C₄	—	2	8	no	—
364	C₄⋊C₄	—	2	8	no	—
365	C₄⋊C₄	—	2	8	no	—
366	C₄⋊C₄	—	2	4	no	—
367	C₄⋊C₄	—	2	4	no	—
368	C₄⋊C₄	—	2	2	no	—
369	C₄⋊C₄	—	2	4	no	—
370	C₄⋊C₄	—	2	1	no	—
371	C₄⋊C₄	—	2	2	no	—
372	C₄⋊C₄	—	2	1	no	—
373	C₄⋊C₄	—	2	1	no	—
374	C₄⋊C₄	—	2	2	no	—
375	C₄⋊C₄	—	2	2	no	—
376	C₄⋊C₄	—	4	4	no	—
377	C₄⋊C₄	—	4	2	no	—
378	C₄⋊C₄	C₂×C₅×D₄	1	2	yes	—
379	C₄⋊C₄	C₂×C₅×D₄	1	4	yes	—
380	C₄²	—	2	8	no	—
381	C₄²	—	2	4	no	—
382	C₄²	—	2	2	no	—
383	C₄²	—	2	2	no	—
384	C₄²	—	4	2	no	—
385	C₄²	C₂×C₅×D₄	1	2	yes	—
386	C₄²	C₂×C₅×D₄	1	2	yes	—
387	C₂×C₅	#2409	1	1	yes	characteristic
388	C₂×C₅	#3005	1	1	yes	characteristic
389	C₂×C₅	#3011	1	1	yes	characteristic
390	C₂×C₅	#3377	1	2	yes	—
391	C₂×C₅	#3390	1	2	yes	—
392	C₂³	C₂²×C₅×D₄	1	1	yes	characteristic
393	Q₈	—	2	2	no	—
394	Q₈	—	2	2	no	—
395	Q₈	—	2	2	no	—
396	Q₈	—	2	2	no	—
397	Q₈	—	2	2	no	—
398	Q₈	—	4	4	no	—
399	Q₈	—	4	8	no	—
400	Q₈	—	4	1	no	—
401	Q₈	—	4	1	no	—
402	Q₈	C₅×C₂²⋊Q₈	1	4	yes	—
403	C₂×C₄	—	2	2	no	—
404	C₂×C₄	—	2	2	no	—
405	C₂×C₄	—	2	2	no	—
406	C₂×C₄	—	2	2	no	—
407	C₂×C₄	—	2	2	no	—
408	C₂×C₄	—	2	2	no	—
409	C₂×C₄	—	2	2	no	—
410	C₂×C₄	—	2	2	no	—
411	C₂×C₄	—	2	4	no	—
412	C₂×C₄	—	2	2	no	—
413	C₂×C₄	—	2	2	no	—
414	C₂×C₄	—	2	2	no	—
415	C₂×C₄	—	2	4	no	—
416	C₂×C₄	—	4	1	no	—
417	C₂×C₄	—	4	1	no	—
418	C₂×C₄	—	4	4	no	—
419	C₂×C₄	—	4	2	no	—
420	C₂×C₄	—	4	1	no	—
421	C₂×C₄	—	4	2	no	—
422	C₂×C₄	—	4	2	no	—
423	C₂×C₄	—	4	2	no	—
424	C₂×C₄	—	4	2	no	—
425	C₂×C₄	C₅×#120	1	2	yes	—
426	C₂×C₄	C₅×#120	1	2	yes	—
427	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
428	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
429	C₂×C₄	C₂²×C₅×Q₈	1	1	yes	characteristic
430	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
431	C₂×C₄	C₅×2₋¹⁺⁴	1	1	yes	characteristic
432	C₂×C₄	C₅×2₋¹⁺⁴	1	1	yes	characteristic
433	C₈	—	2	2	no	—
434	C₈	—	4	1	no	—
435	C₈	—	4	2	no	—
436	C₅	#24344	1	1	yes	characteristic, direct product factor, Sylow
437	C₂²	C₂×C₅×#120	1	1	yes	characteristic
438	C₂²	C₅×#548	1	1	yes	characteristic
439	C₂²	C₅×D₄×Q₈	1	1	yes	characteristic
440	C₂²	C₅×#575	1	2	yes	—
441	C₂²	C₅×#578	1	2	yes	—
442	C₄	—	2	2	no	—
443	C₄	—	2	2	no	—
444	C₄	—	2	4	no	—
445	C₄	—	4	2	no	—
446	C₄	—	4	4	no	—
447	C₄	—	4	2	no	—
448	C₄	—	4	2	no	—
449	C₄	—	4	2	no	—
450	C₄	—	8	1	no	—
451	C₄	—	8	2	no	—
452	C₄	C₂×C₅×C₂²⋊Q₈	1	1	yes	characteristic
453	C₄	C₅×#536	1	1	yes	characteristic
454	C₄	C₅×#548	1	1	yes	characteristic
455	C₄	C₅×D₄×Q₈	1	1	yes	characteristic
456	C₂	C₅×#2409	1	1	yes	characteristic
457	C₂	C₅×#3005	1	1	yes	characteristic
458	C₂	C₅×#3011	1	1	yes	characteristic
459	C₂	C₅×#3377	1	2	yes	—
460	C₂	C₅×#3390	1	2	yes	—

	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 ◁ C₂×C₄×C₅×Q₈ ◁ G

Complements

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

N	H ≅ G/N	type
45. #24344	C₅	direct (N × H)
52. C₂×C₅×Q₁₆	Q₈	semidirect
257. C₂×Q₁₆	C₅×Q₈	semidirect
436. C₅	#24344	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×#557	2
C₂×C₅×#477	2
C₂×C₅×#441	2
C₅×#2581	2
C₅×#2059	2
C₅×#2026	2
C₅×#1993	2
C₅×#1985	2
C₅×#1878	2
C₅×#1863	2
C₅×#1805	2
#24344	5

Subgroups — C5×#24344 #11947064

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#24344 #11947064