Subgroups — C₅×#24333 #11947053

Order 1280.

1034 conjugacy classes of subgroups.

The subgroup lattice has 496 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×Q₈²	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅×#477	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄×C₅×Q₁₆	C₂	1	1	yes	maximal, characteristic
4	C₅×#2582	C₂	1	1	yes	maximal, characteristic
5	C₅×#2057	C₂	1	2	yes	maximal
6	C₅×#2024	C₂	1	2	yes	maximal
7	C₅×#1990	C₂	1	1	yes	maximal, characteristic
8	C₅×#1984	C₂	1	1	yes	maximal, characteristic
9	C₅×#1878	C₂	1	2	yes	maximal
10	C₅×#1863	C₂	1	2	yes	maximal
11	C₅×#1803	C₂	1	1	yes	maximal, characteristic
12	C₂²×C₅×Q₁₆	C₂²	1	1	yes	characteristic
13	C₅×Q₈²	—	2	4	no	—
14	C₅×Q₈²	—	2	4	no	—
15	C₂×C₅×C₄⋊Q₈	—	2	1	no	—
16	C₂×C₅×C₄⋊Q₈	—	2	2	no	—
17	C₂×C₅×C₄⋊Q₈	C₂²	1	2	yes	—
18	C₂×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
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	C₄×C₅×Q₁₆	—	2	4	no	—
26	C₂×C₅×#107	C₂²	1	1	yes	characteristic
27	C₂×C₅×#107	C₂²	1	2	yes	—
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×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
34	C₅×#398	—	2	2	no	—
35	C₅×#391	—	2	1	no	—
36	C₅×#391	C₂²	1	2	yes	—
37	C₅×#389	—	2	1	no	—
38	C₅×#389	C₂²	1	2	yes	—
39	C₅×#384	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	#24333	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
46	C₂²×C₅×Q₈	—	2	2	no	—
47	C₂²×C₅×Q₈	—	2	1	no	—
48	C₂²×C₅×Q₈	D₄	1	1	yes	characteristic
49	C₂²×C₅×Q₈	C₂³	1	1	yes	characteristic
50	C₂²×C₅×Q₈	C₂³	1	1	yes	characteristic
51	C₂×C₅×Q₁₆	—	2	2	no	—
52	C₂×C₅×Q₁₆	—	2	2	no	—
53	C₂×C₅×Q₁₆	Q₈	1	4	yes	complemented
54	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
55	C₂²×C₅×C₈	C₂³	1	2	yes	—
56	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
57	C₅×C₄⋊Q₈	—	2	16	no	—
58	C₅×C₄⋊Q₈	—	2	8	no	—
59	C₅×C₄⋊Q₈	—	2	4	no	—
60	C₅×C₄⋊Q₈	—	2	4	no	—
61	C₅×C₄⋊Q₈	—	2	2	no	—
62	C₅×C₄⋊Q₈	D₄	1	4	yes	—
63	C₄×C₅×Q₈	—	2	8	no	—
64	C₄×C₅×Q₈	—	2	4	no	—
65	C₄×C₅×Q₈	—	2	4	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	—	2	2	no	—
71	C₄×C₅×Q₈	D₄	1	4	yes	—
72	C₂×C₅×C₄⋊C₄	—	2	2	no	—
73	C₂×C₅×C₄⋊C₄	—	2	1	no	—
74	C₂×C₅×C₄⋊C₄	—	2	2	no	—
75	C₂×C₅×C₄⋊C₄	—	2	1	no	—
76	C₂×C₅×C₄⋊C₄	—	2	1	no	—
77	C₂×C₅×C₄⋊C₄	—	2	1	no	—
78	C₂×C₅×C₄⋊C₄	—	2	1	no	—
79	C₂×C₅×C₄⋊C₄	—	2	2	no	—
80	C₂×C₅×C₄⋊C₄	D₄	1	1	yes	characteristic
81	C₂×C₅×C₄⋊C₄	D₄	1	2	yes	—
82	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
83	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
84	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
85	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
86	C₂×C₄²×C₅	—	2	2	no	—
87	C₂×C₄²×C₅	—	2	1	no	—
88	C₂×C₄²×C₅	—	2	1	no	—
89	C₂×C₄²×C₅	C₂³	1	2	yes	—
90	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
91	C₅×#107	—	2	2	no	—
92	C₅×#107	—	2	4	no	—
93	C₅×C₄⋊C₈	—	2	2	no	—
94	C₅×#103	—	2	2	no	—
95	C₅×#103	—	2	4	no	—
96	C₅×#103	—	2	2	no	—
97	C₅×#103	—	2	4	no	—
98	C₄×C₅×C₈	—	2	2	no	—
99	C₅×#95	—	2	2	no	—
100	C₅×#95	—	2	2	no	—
101	C₅×#95	—	2	2	no	—
102	C₂×Q₈²	C₂×C₅	1	1	yes	characteristic
103	C₂×#477	C₂×C₅	1	1	yes	characteristic
104	C₂×C₄×Q₁₆	C₂×C₅	1	1	yes	characteristic
105	#2582	C₂×C₅	1	1	yes	characteristic
106	#2057	C₂×C₅	1	2	yes	—
107	#2024	C₂×C₅	1	2	yes	—
108	#1990	C₂×C₅	1	1	yes	characteristic
109	#1984	C₂×C₅	1	1	yes	characteristic
110	#1878	C₂×C₅	1	2	yes	—
111	#1863	C₂×C₅	1	2	yes	—
112	#1803	C₂×C₅	1	1	yes	characteristic
113	C₂×C₅×Q₈	—	2	8	no	—
114	C₂×C₅×Q₈	—	2	2	no	—
115	C₂×C₅×Q₈	—	2	4	no	—
116	C₂×C₅×Q₈	—	2	2	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	—	2	1	no	—
124	C₂×C₅×Q₈	—	2	1	no	—
125	C₂×C₅×Q₈	—	8	1	no	—
126	C₂×C₅×Q₈	—	8	1	no	—
127	C₂×C₅×Q₈	—	8	2	no	—
128	C₂×C₅×Q₈	—	8	2	no	—
129	C₂×C₅×Q₈	Q₁₆	1	4	yes	complemented
130	C₂×C₅×Q₈	C₂×D₄	1	2	yes	—
131	C₂×C₅×Q₈	C₂×Q₈	1	2	yes	—
132	C₂×C₅×Q₈	C₂×Q₈	1	2	yes	—
133	C₂×C₅×Q₈	#41	1	2	yes	—
134	C₂²×C₄×C₅	—	2	1	no	—
135	C₂²×C₄×C₅	—	2	2	no	—
136	C₂²×C₄×C₅	—	2	1	no	—
137	C₂²×C₄×C₅	—	2	1	no	—
138	C₂²×C₄×C₅	—	2	1	no	—
139	C₂²×C₄×C₅	—	2	2	no	—
140	C₂²×C₄×C₅	C₂×D₄	1	2	yes	—
141	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
142	C₂²×C₄×C₅	C₂×D₄	1	2	yes	—
143	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
144	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
145	C₅×Q₁₆	—	2	8	no	—
146	C₂×C₅×C₈	—	2	1	no	—
147	C₂×C₅×C₈	—	2	1	no	—
148	C₂×C₅×C₈	—	2	1	no	—
149	C₂×C₅×C₈	—	2	2	no	—
150	C₂×C₅×C₈	—	2	2	no	—
151	C₂×C₅×C₈	—	2	1	no	—
152	C₂×C₅×C₈	—	2	1	no	—
153	C₂×C₅×C₈	—	2	2	no	—
154	C₂×C₅×C₈	C₂×Q₈	1	2	yes	—
155	C₅×C₄⋊C₄	—	2	8	no	—
156	C₅×C₄⋊C₄	—	2	8	no	—
157	C₅×C₄⋊C₄	—	2	4	no	—
158	C₅×C₄⋊C₄	—	2	4	no	—
159	C₅×C₄⋊C₄	—	2	4	no	—
160	C₅×C₄⋊C₄	—	2	2	no	—
161	C₅×C₄⋊C₄	—	2	2	no	—
162	C₅×C₄⋊C₄	—	2	1	no	—
163	C₅×C₄⋊C₄	—	2	1	no	—
164	C₅×C₄⋊C₄	—	2	1	no	—
165	C₅×C₄⋊C₄	—	2	2	no	—
166	C₅×C₄⋊C₄	—	2	2	no	—
167	C₅×C₄⋊C₄	—	4	2	no	—
168	C₅×C₄⋊C₄	—	4	2	no	—
169	C₅×C₄⋊C₄	—	8	1	no	—
170	C₅×C₄⋊C₄	—	8	2	no	—
171	C₅×C₄⋊C₄	C₂×D₄	1	4	yes	—
172	C₅×C₄⋊C₄	C₂×D₄	1	2	yes	—
173	C₄²×C₅	—	2	8	no	—
174	C₄²×C₅	—	2	4	no	—
175	C₄²×C₅	—	2	2	no	—
176	C₄²×C₅	—	2	2	no	—
177	C₄²×C₅	—	4	2	no	—
178	C₄²×C₅	C₂×D₄	1	2	yes	—
179	C₄²×C₅	C₂×D₄	1	2	yes	—
180	C₂²×Q₁₆	C₂²×C₅	1	1	yes	characteristic
181	Q₈²	—	2	4	no	—
182	Q₈²	—	2	4	no	—
183	C₂×C₄⋊Q₈	—	2	1	no	—
184	C₂×C₄⋊Q₈	—	2	2	no	—
185	C₂×C₄⋊Q₈	C₂²×C₅	1	2	yes	—
186	C₂×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
187	C₂×C₄×Q₈	—	2	1	no	—
188	C₂×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
189	C₂×C₄×Q₈	C₂²×C₅	1	2	yes	—
190	C₂×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
191	C₂×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
192	#477	—	2	4	no	—
193	C₄×Q₁₆	—	2	4	no	—
194	C₂×#107	C₂²×C₅	1	2	yes	—
195	C₂×#107	C₂²×C₅	1	1	yes	characteristic
196	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
197	C₂×#103	C₂²×C₅	1	2	yes	—
198	C₂×#103	C₂²×C₅	1	2	yes	—
199	C₂×#103	C₂²×C₅	1	1	yes	characteristic
200	C₂×#103	C₂²×C₅	1	1	yes	characteristic
201	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
202	#398	—	2	2	no	—
203	#391	—	2	1	no	—
204	#391	C₂²×C₅	1	2	yes	—
205	#389	—	2	1	no	—
206	#389	C₂²×C₅	1	2	yes	—
207	#384	C₂²×C₅	1	1	yes	characteristic
208	#340	C₂²×C₅	1	2	yes	—
209	#340	C₂²×C₅	1	2	yes	—
210	#340	C₂²×C₅	1	2	yes	—
211	#336	C₂²×C₅	1	2	yes	—
212	#336	C₂²×C₅	1	2	yes	—
213	C₂³×C₅	C₂²×D₄	1	1	yes	characteristic
214	C₅×Q₈	—	2	2	no	—
215	C₅×Q₈	—	2	2	no	—
216	C₅×Q₈	—	2	2	no	—
217	C₅×Q₈	—	2	8	no	—
218	C₅×Q₈	—	2	2	no	—
219	C₅×Q₈	—	2	2	no	—
220	C₅×Q₈	—	4	1	no	—
221	C₅×Q₈	—	4	1	no	—
222	C₅×Q₈	—	8	4	no	—
223	C₅×Q₈	—	8	8	no	—
224	C₅×Q₈	C₂²⋊Q₈	1	4	yes	—
225	C₂×C₄×C₅	—	2	2	no	—
226	C₂×C₄×C₅	—	2	2	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	1	no	—
231	C₂×C₄×C₅	—	2	1	no	—
232	C₂×C₄×C₅	—	2	2	no	—
233	C₂×C₄×C₅	—	2	4	no	—
234	C₂×C₄×C₅	—	2	2	no	—
235	C₂×C₄×C₅	—	2	2	no	—
236	C₂×C₄×C₅	—	2	2	no	—
237	C₂×C₄×C₅	—	2	2	no	—
238	C₂×C₄×C₅	—	4	1	no	—
239	C₂×C₄×C₅	—	4	1	no	—
240	C₂×C₄×C₅	—	4	2	no	—
241	C₂×C₄×C₅	—	4	1	no	—
242	C₂×C₄×C₅	—	4	2	no	—
243	C₂×C₄×C₅	—	4	1	no	—
244	C₂×C₄×C₅	—	4	1	no	—
245	C₂×C₄×C₅	—	4	2	no	—
246	C₂×C₄×C₅	—	4	2	no	—
247	C₂×C₄×C₅	—	4	2	no	—
248	C₂×C₄×C₅	—	4	1	no	—
249	C₂×C₄×C₅	—	4	1	no	—
250	C₂×C₄×C₅	#120	1	2	yes	—
251	C₂×C₄×C₅	#120	1	2	yes	—
252	C₂×C₄×C₅	C₂×Q₁₆	1	4	yes	—
253	C₂×C₄×C₅	C₂×Q₁₆	1	2	yes	—
254	C₂×C₄×C₅	#137	1	2	yes	—
255	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
256	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
257	C₂×C₄×C₅	C₂²×Q₈	1	1	yes	characteristic
258	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
259	C₂×C₄×C₅	2₋¹⁺⁴	1	1	yes	characteristic
260	C₂×C₄×C₅	2₋¹⁺⁴	1	1	yes	characteristic
261	C₅×C₈	—	2	2	no	—
262	C₅×C₈	—	4	1	no	—
263	C₅×C₈	—	4	2	no	—
264	C₂²×Q₈	—	2	2	no	—
265	C₂²×Q₈	—	2	1	no	—
266	C₂²×Q₈	C₅×D₄	1	1	yes	characteristic
267	C₂²×Q₈	C₂³×C₅	1	1	yes	characteristic
268	C₂²×Q₈	C₂³×C₅	1	1	yes	characteristic
269	C₂×Q₁₆	—	2	2	no	—
270	C₂×Q₁₆	—	2	2	no	—
271	C₂×Q₁₆	C₅×Q₈	1	4	yes	complemented
272	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
273	C₂²×C₈	C₂³×C₅	1	2	yes	—
274	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
275	C₄⋊Q₈	—	2	16	no	—
276	C₄⋊Q₈	—	2	8	no	—
277	C₄⋊Q₈	—	2	4	no	—
278	C₄⋊Q₈	—	2	4	no	—
279	C₄⋊Q₈	—	2	2	no	—
280	C₄⋊Q₈	C₅×D₄	1	4	yes	—
281	C₄×Q₈	—	2	8	no	—
282	C₄×Q₈	—	2	4	no	—
283	C₄×Q₈	—	2	4	no	—
284	C₄×Q₈	—	2	2	no	—
285	C₄×Q₈	—	2	2	no	—
286	C₄×Q₈	—	2	2	no	—
287	C₄×Q₈	—	2	2	no	—
288	C₄×Q₈	—	2	2	no	—
289	C₄×Q₈	C₅×D₄	1	4	yes	—
290	C₂×C₄⋊C₄	—	2	2	no	—
291	C₂×C₄⋊C₄	—	2	1	no	—
292	C₂×C₄⋊C₄	—	2	2	no	—
293	C₂×C₄⋊C₄	—	2	1	no	—
294	C₂×C₄⋊C₄	—	2	1	no	—
295	C₂×C₄⋊C₄	—	2	1	no	—
296	C₂×C₄⋊C₄	—	2	1	no	—
297	C₂×C₄⋊C₄	—	2	2	no	—
298	C₂×C₄⋊C₄	C₅×D₄	1	1	yes	characteristic
299	C₂×C₄⋊C₄	C₅×D₄	1	2	yes	—
300	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
301	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
302	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
303	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
304	C₂×C₄²	—	2	2	no	—
305	C₂×C₄²	—	2	1	no	—
306	C₂×C₄²	—	2	1	no	—
307	C₂×C₄²	C₂³×C₅	1	2	yes	—
308	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
309	#107	—	2	2	no	—
310	#107	—	2	4	no	—
311	C₄⋊C₈	—	2	2	no	—
312	#103	—	2	2	no	—
313	#103	—	2	4	no	—
314	#103	—	2	2	no	—
315	#103	—	2	4	no	—
316	C₄×C₈	—	2	2	no	—
317	#95	—	2	2	no	—
318	#95	—	2	2	no	—
319	#95	—	2	2	no	—
320	C₂²×C₅	C₂×#120	1	1	yes	characteristic
321	C₂²×C₅	#548	1	1	yes	characteristic
322	C₂²×C₅	D₄×Q₈	1	1	yes	characteristic
323	C₂²×C₅	C₂²×Q₁₆	1	1	yes	characteristic
324	C₂²×C₅	C₂×#137	1	1	yes	characteristic
325	C₂²×C₅	#576	1	1	yes	characteristic
326	C₂²×C₅	#577	1	1	yes	characteristic
327	C₄×C₅	—	2	4	no	—
328	C₄×C₅	—	2	4	no	—
329	C₄×C₅	—	2	2	no	—
330	C₄×C₅	—	4	2	no	—
331	C₄×C₅	—	4	2	no	—
332	C₄×C₅	—	4	4	no	—
333	C₄×C₅	—	4	2	no	—
334	C₄×C₅	—	8	2	no	—
335	C₄×C₅	—	8	1	no	—
336	C₄×C₅	#451	1	4	yes	—
337	C₄×C₅	C₂×C₂²⋊Q₈	1	1	yes	characteristic
338	C₄×C₅	#536	1	1	yes	characteristic
339	C₄×C₅	#548	1	1	yes	characteristic
340	C₄×C₅	D₄×Q₈	1	1	yes	characteristic
341	C₂×Q₈	—	2	8	no	—
342	C₂×Q₈	—	2	2	no	—
343	C₂×Q₈	—	2	4	no	—
344	C₂×Q₈	—	2	2	no	—
345	C₂×Q₈	—	2	1	no	—
346	C₂×Q₈	—	2	1	no	—
347	C₂×Q₈	—	2	1	no	—
348	C₂×Q₈	—	2	1	no	—
349	C₂×Q₈	—	2	1	no	—
350	C₂×Q₈	—	2	1	no	—
351	C₂×Q₈	—	2	1	no	—
352	C₂×Q₈	—	2	1	no	—
353	C₂×Q₈	—	8	1	no	—
354	C₂×Q₈	—	8	1	no	—
355	C₂×Q₈	—	8	2	no	—
356	C₂×Q₈	—	8	2	no	—
357	C₂×Q₈	C₅×Q₁₆	1	4	yes	complemented
358	C₂×Q₈	C₂×C₅×D₄	1	2	yes	—
359	C₂×Q₈	C₂×C₅×Q₈	1	2	yes	—
360	C₂×Q₈	C₂×C₅×Q₈	1	2	yes	—
361	C₂×Q₈	C₅×#41	1	2	yes	—
362	C₂²×C₄	—	2	1	no	—
363	C₂²×C₄	—	2	1	no	—
364	C₂²×C₄	—	2	2	no	—
365	C₂²×C₄	—	2	1	no	—
366	C₂²×C₄	—	2	2	no	—
367	C₂²×C₄	—	2	1	no	—
368	C₂²×C₄	C₂×C₅×D₄	1	2	yes	—
369	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
370	C₂²×C₄	C₂×C₅×D₄	1	2	yes	—
371	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
372	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
373	Q₁₆	—	2	8	no	—
374	C₂×C₈	—	2	1	no	—
375	C₂×C₈	—	2	1	no	—
376	C₂×C₈	—	2	1	no	—
377	C₂×C₈	—	2	2	no	—
378	C₂×C₈	—	2	2	no	—
379	C₂×C₈	—	2	1	no	—
380	C₂×C₈	—	2	1	no	—
381	C₂×C₈	—	2	2	no	—
382	C₂×C₈	C₂×C₅×Q₈	1	2	yes	—
383	C₄⋊C₄	—	2	8	no	—
384	C₄⋊C₄	—	2	8	no	—
385	C₄⋊C₄	—	2	4	no	—
386	C₄⋊C₄	—	2	4	no	—
387	C₄⋊C₄	—	2	4	no	—
388	C₄⋊C₄	—	2	2	no	—
389	C₄⋊C₄	—	2	2	no	—
390	C₄⋊C₄	—	2	1	no	—
391	C₄⋊C₄	—	2	1	no	—
392	C₄⋊C₄	—	2	1	no	—
393	C₄⋊C₄	—	2	2	no	—
394	C₄⋊C₄	—	2	2	no	—
395	C₄⋊C₄	—	4	2	no	—
396	C₄⋊C₄	—	4	2	no	—
397	C₄⋊C₄	—	8	1	no	—
398	C₄⋊C₄	—	8	2	no	—
399	C₄⋊C₄	C₂×C₅×D₄	1	4	yes	—
400	C₄⋊C₄	C₂×C₅×D₄	1	2	yes	—
401	C₄²	—	2	8	no	—
402	C₄²	—	2	4	no	—
403	C₄²	—	2	2	no	—
404	C₄²	—	2	2	no	—
405	C₄²	—	4	2	no	—
406	C₄²	C₂×C₅×D₄	1	2	yes	—
407	C₄²	C₂×C₅×D₄	1	2	yes	—
408	C₂×C₅	#2409	1	1	yes	characteristic
409	C₂×C₅	C₂×#451	1	1	yes	characteristic
410	C₂×C₅	#3012	1	1	yes	characteristic
411	C₂×C₅	#3363	1	1	yes	characteristic
412	C₂×C₅	#3375	1	1	yes	characteristic
413	C₂×C₅	Q₈×Q₁₆	1	1	yes	characteristic
414	C₂×C₅	#3387	1	1	yes	characteristic
415	C₂³	C₂²×C₅×D₄	1	1	yes	characteristic
416	Q₈	—	2	8	no	—
417	Q₈	—	2	2	no	—
418	Q₈	—	2	2	no	—
419	Q₈	—	2	2	no	—
420	Q₈	—	2	2	no	—
421	Q₈	—	2	2	no	—
422	Q₈	—	4	1	no	—
423	Q₈	—	4	1	no	—
424	Q₈	—	8	4	no	—
425	Q₈	—	8	8	no	—
426	Q₈	C₅×C₂²⋊Q₈	1	4	yes	—
427	C₂×C₄	—	2	2	no	—
428	C₂×C₄	—	2	2	no	—
429	C₂×C₄	—	2	2	no	—
430	C₂×C₄	—	2	2	no	—
431	C₂×C₄	—	2	2	no	—
432	C₂×C₄	—	2	1	no	—
433	C₂×C₄	—	2	1	no	—
434	C₂×C₄	—	2	2	no	—
435	C₂×C₄	—	2	4	no	—
436	C₂×C₄	—	2	2	no	—
437	C₂×C₄	—	2	2	no	—
438	C₂×C₄	—	2	2	no	—
439	C₂×C₄	—	2	2	no	—
440	C₂×C₄	—	4	1	no	—
441	C₂×C₄	—	4	1	no	—
442	C₂×C₄	—	4	2	no	—
443	C₂×C₄	—	4	1	no	—
444	C₂×C₄	—	4	2	no	—
445	C₂×C₄	—	4	1	no	—
446	C₂×C₄	—	4	1	no	—
447	C₂×C₄	—	4	2	no	—
448	C₂×C₄	—	4	2	no	—
449	C₂×C₄	—	4	1	no	—
450	C₂×C₄	—	4	2	no	—
451	C₂×C₄	—	4	1	no	—
452	C₂×C₄	C₅×#120	1	2	yes	—
453	C₂×C₄	C₅×#120	1	2	yes	—
454	C₂×C₄	C₂×C₅×Q₁₆	1	4	yes	—
455	C₂×C₄	C₂×C₅×Q₁₆	1	2	yes	—
456	C₂×C₄	C₅×#137	1	2	yes	—
457	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
458	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
459	C₂×C₄	C₂²×C₅×Q₈	1	1	yes	characteristic
460	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
461	C₂×C₄	C₅×2₋¹⁺⁴	1	1	yes	characteristic
462	C₂×C₄	C₅×2₋¹⁺⁴	1	1	yes	characteristic
463	C₈	—	2	2	no	—
464	C₈	—	4	1	no	—
465	C₈	—	4	2	no	—
466	C₅	#24333	1	1	yes	characteristic, direct product factor, Sylow
467	C₂²	C₂×C₅×#120	1	1	yes	characteristic
468	C₂²	C₅×#548	1	1	yes	characteristic
469	C₂²	C₅×D₄×Q₈	1	1	yes	characteristic
470	C₂²	C₂²×C₅×Q₁₆	1	1	yes	characteristic
471	C₂²	C₂×C₅×#137	1	1	yes	characteristic
472	C₂²	C₅×#576	1	1	yes	characteristic
473	C₂²	C₅×#577	1	1	yes	characteristic
474	C₄	—	2	4	no	—
475	C₄	—	2	2	no	—
476	C₄	—	2	4	no	—
477	C₄	—	4	2	no	—
478	C₄	—	4	4	no	—
479	C₄	—	4	2	no	—
480	C₄	—	4	2	no	—
481	C₄	—	8	1	no	—
482	C₄	—	8	2	no	—
483	C₄	C₅×#451	1	4	yes	—
484	C₄	C₂×C₅×C₂²⋊Q₈	1	1	yes	characteristic
485	C₄	C₅×#536	1	1	yes	characteristic
486	C₄	C₅×#548	1	1	yes	characteristic
487	C₄	C₅×D₄×Q₈	1	1	yes	characteristic
488	C₂	C₅×#2409	1	1	yes	characteristic
489	C₂	C₂×C₅×#451	1	1	yes	characteristic
490	C₂	C₅×#3012	1	1	yes	characteristic
491	C₂	C₅×#3363	1	1	yes	characteristic
492	C₂	C₅×#3375	1	1	yes	characteristic
493	C₂	C₅×Q₈×Q₁₆	1	1	yes	characteristic
494	C₂	C₅×#3387	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 ◁ C₂×C₄×C₅×Q₈ ◁ G

Complements

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

N	H ≅ G/N	type
45. #24333	C₅	direct (N × H)
53. C₂×C₅×Q₁₆	Q₈	semidirect
129. C₂×C₅×Q₈	Q₁₆	semidirect
271. C₂×Q₁₆	C₅×Q₈	semidirect
357. C₂×Q₈	C₅×Q₁₆	semidirect
466. C₅	#24333	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×Q₈²	2
C₂×C₅×#477	2
C₂×C₄×C₅×Q₁₆	2
C₅×#2582	2
C₅×#2057	2
C₅×#2024	2
C₅×#1990	2
C₅×#1984	2
C₅×#1878	2
C₅×#1863	2
C₅×#1803	2
#24333	5

Subgroups — C5×#24333 #11947053

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#24333 #11947053