Subgroups — C₅×#11378 #11934098

Order 1280.

814 conjugacy classes of subgroups.

The subgroup lattice has 538 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₅×#106	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅×#340	C₂	1	1	yes	maximal, characteristic
3	C₂×C₅×#340	C₂	1	1	yes	maximal, characteristic
4	C₂×C₅×#340	C₂	1	1	yes	maximal, characteristic
5	C₂×C₅×#336	C₂	1	1	yes	maximal, characteristic
6	C₅×C₄⋊#95	C₂	1	1	yes	maximal, characteristic
7	C₅×C₄⋊#95	C₂	1	1	yes	maximal, characteristic
8	C₂³×C₅×C₈	C₂²	1	1	yes	characteristic
9	C₂³×C₅×C₈	C₂²	1	1	yes	characteristic
10	C₂²×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
11	C₂²×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
12	C₂²×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
13	C₂²×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
14	C₂²×C₄²×C₅	C₂²	1	1	yes	characteristic
15	C₂×C₅×#106	—	2	2	no	—
16	C₂×C₅×#106	—	2	2	no	—
17	C₂×C₅×#106	C₄	1	4	yes	complemented
18	C₂×C₅×#95	—	2	2	no	—
19	C₂×C₅×#95	—	2	2	no	—
20	C₅×#340	—	2	2	no	—
21	C₅×#340	—	2	2	no	—
22	C₅×#340	—	2	2	no	—
23	C₅×#336	—	2	2	no	—
24	#11378	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
25	C₂³×C₄×C₅	—	2	1	no	—
26	C₂³×C₄×C₅	—	2	1	no	—
27	C₂³×C₄×C₅	—	2	1	no	—
28	C₂³×C₄×C₅	—	2	1	no	—
29	C₂³×C₄×C₅	D₄	1	2	yes	—
30	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
31	C₂²×C₅×C₈	—	2	1	no	—
32	C₂²×C₅×C₈	—	2	1	no	—
33	C₂²×C₅×C₈	—	2	1	no	—
34	C₂²×C₅×C₈	—	2	1	no	—
35	C₂²×C₅×C₈	—	2	1	no	—
36	C₂²×C₅×C₈	—	2	1	no	—
37	C₂²×C₅×C₈	—	2	1	no	—
38	C₂²×C₅×C₈	—	2	1	no	—
39	C₂²×C₅×C₈	—	2	1	no	—
40	C₂²×C₅×C₈	—	2	1	no	—
41	C₂²×C₅×C₈	C₂×C₄	1	2	yes	—
42	C₂²×C₅×C₈	D₄	1	2	yes	—
43	C₂²×C₅×C₈	D₄	1	2	yes	—
44	C₂²×C₅×C₈	D₄	1	2	yes	—
45	C₂×C₅×C₄⋊C₄	—	2	1	no	—
46	C₂×C₅×C₄⋊C₄	—	2	1	no	—
47	C₂×C₅×C₄⋊C₄	—	2	1	no	—
48	C₂×C₅×C₄⋊C₄	—	2	1	no	—
49	C₂×C₅×C₄⋊C₄	—	2	1	no	—
50	C₂×C₅×C₄⋊C₄	—	2	1	no	—
51	C₂×C₅×C₄⋊C₄	—	2	1	no	—
52	C₂×C₅×C₄⋊C₄	—	2	1	no	—
53	C₂×C₅×C₄⋊C₄	—	2	1	no	—
54	C₂×C₅×C₄⋊C₄	—	2	1	no	—
55	C₂×C₅×C₄⋊C₄	—	2	1	no	—
56	C₂×C₅×C₄⋊C₄	—	2	1	no	—
57	C₂×C₅×C₄⋊C₄	—	2	1	no	—
58	C₂×C₅×C₄⋊C₄	—	2	1	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	—	2	1	no	—
63	C₂×C₅×C₄⋊C₄	—	2	1	no	—
64	C₂×C₅×C₄⋊C₄	—	2	1	no	—
65	C₂×C₅×C₄⋊C₄	C₂×C₄	1	2	yes	—
66	C₂×C₅×C₄⋊C₄	C₂×C₄	1	2	yes	—
67	C₂×C₅×C₄⋊C₄	Q₈	1	2	yes	—
68	C₂×C₅×C₄⋊C₄	Q₈	1	2	yes	—
69	C₂×C₄²×C₅	—	2	1	no	—
70	C₂×C₄²×C₅	—	2	1	no	—
71	C₂×C₄²×C₅	—	2	1	no	—
72	C₂×C₄²×C₅	—	2	1	no	—
73	C₂×C₄²×C₅	—	2	1	no	—
74	C₂×C₄²×C₅	—	2	1	no	—
75	C₅×#106	—	2	8	no	—
76	C₅×#95	—	4	4	no	—
77	C₅×#95	—	4	4	no	—
78	C₂²×#106	C₂×C₅	1	1	yes	characteristic
79	C₂×#340	C₂×C₅	1	1	yes	characteristic
80	C₂×#340	C₂×C₅	1	1	yes	characteristic
81	C₂×#340	C₂×C₅	1	1	yes	characteristic
82	C₂×#336	C₂×C₅	1	1	yes	characteristic
83	C₄⋊#95	C₂×C₅	1	1	yes	characteristic
84	C₄⋊#95	C₂×C₅	1	1	yes	characteristic
85	C₂⁴×C₅	C₂×D₄	1	1	yes	characteristic
86	C₂²×C₄×C₅	—	2	2	no	—
87	C₂²×C₄×C₅	—	2	2	no	—
88	C₂²×C₄×C₅	—	2	2	no	—
89	C₂²×C₄×C₅	—	2	2	no	—
90	C₂²×C₄×C₅	—	2	2	no	—
91	C₂²×C₄×C₅	—	2	2	no	—
92	C₂²×C₄×C₅	—	2	2	no	—
93	C₂²×C₄×C₅	—	2	2	no	—
94	C₂²×C₄×C₅	—	2	2	no	—
95	C₂²×C₄×C₅	—	2	2	no	—
96	C₂²×C₄×C₅	—	4	1	no	—
97	C₂²×C₄×C₅	—	4	1	no	—
98	C₂²×C₄×C₅	—	4	1	no	—
99	C₂²×C₄×C₅	—	4	1	no	—
100	C₂²×C₄×C₅	—	4	1	no	—
101	C₂²×C₄×C₅	—	4	1	no	—
102	C₂²×C₄×C₅	—	4	1	no	—
103	C₂²×C₄×C₅	—	4	1	no	—
104	C₂²×C₄×C₅	—	4	2	no	—
105	C₂²×C₄×C₅	—	4	2	no	—
106	C₂²×C₄×C₅	—	4	2	no	—
107	C₂²×C₄×C₅	—	4	2	no	—
108	C₂²×C₄×C₅	—	4	2	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	SD₁₆	1	4	yes	—
113	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
114	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
115	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
116	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
117	C₂²×C₄×C₅	C₂×Q₈	1	1	yes	characteristic
118	C₂²×C₄×C₅	C₂×Q₈	1	1	yes	characteristic
119	C₂²×C₄×C₅	#41	1	1	yes	characteristic
120	C₂²×C₄×C₅	#41	1	1	yes	characteristic
121	C₂²×C₄×C₅	#41	1	1	yes	characteristic
122	C₂²×C₄×C₅	#41	1	1	yes	characteristic
123	C₂²×C₄×C₅	#41	1	1	yes	characteristic
124	C₂²×C₄×C₅	#41	1	1	yes	characteristic
125	C₂²×C₄×C₅	#41	1	1	yes	characteristic
126	C₂²×C₄×C₅	#41	1	1	yes	characteristic
127	C₂×C₅×C₈	—	2	2	no	—
128	C₂×C₅×C₈	—	2	2	no	—
129	C₂×C₅×C₈	—	2	2	no	—
130	C₂×C₅×C₈	—	2	2	no	—
131	C₂×C₅×C₈	—	2	2	no	—
132	C₂×C₅×C₈	—	2	2	no	—
133	C₂×C₅×C₈	—	2	2	no	—
134	C₂×C₅×C₈	—	2	2	no	—
135	C₂×C₅×C₈	—	2	2	no	—
136	C₂×C₅×C₈	—	4	1	no	—
137	C₂×C₅×C₈	—	4	1	no	—
138	C₂×C₅×C₈	—	4	1	no	—
139	C₂×C₅×C₈	—	4	1	no	—
140	C₂×C₅×C₈	C₂²⋊C₄	1	4	yes	—
141	C₅×C₄⋊C₄	—	2	2	no	—
142	C₅×C₄⋊C₄	—	2	2	no	—
143	C₅×C₄⋊C₄	—	2	2	no	—
144	C₅×C₄⋊C₄	—	2	2	no	—
145	C₅×C₄⋊C₄	—	2	2	no	—
146	C₅×C₄⋊C₄	—	2	2	no	—
147	C₅×C₄⋊C₄	—	2	2	no	—
148	C₅×C₄⋊C₄	—	2	2	no	—
149	C₅×C₄⋊C₄	—	4	1	no	—
150	C₅×C₄⋊C₄	—	4	1	no	—
151	C₅×C₄⋊C₄	—	4	1	no	—
152	C₅×C₄⋊C₄	—	4	1	no	—
153	C₅×C₄⋊C₄	—	4	1	no	—
154	C₅×C₄⋊C₄	—	4	1	no	—
155	C₅×C₄⋊C₄	—	4	1	no	—
156	C₅×C₄⋊C₄	—	4	1	no	—
157	C₄²×C₅	—	4	1	no	—
158	C₄²×C₅	—	4	1	no	—
159	C₄²×C₅	—	4	1	no	—
160	C₄²×C₅	—	4	1	no	—
161	C₂³×C₈	C₂²×C₅	1	1	yes	characteristic
162	C₂³×C₈	C₂²×C₅	1	1	yes	characteristic
163	C₂²×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
164	C₂²×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
165	C₂²×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
166	C₂²×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
167	C₂²×C₄²	C₂²×C₅	1	1	yes	characteristic
168	C₂×#106	—	2	2	no	—
169	C₂×#106	—	2	2	no	—
170	C₂×#106	C₄×C₅	1	4	yes	complemented
171	C₂×#95	—	2	2	no	—
172	C₂×#95	—	2	2	no	—
173	#340	—	2	2	no	—
174	#340	—	2	2	no	—
175	#340	—	2	2	no	—
176	#336	—	2	2	no	—
177	C₂³×C₅	C₄×D₄	1	1	yes	characteristic
178	C₂³×C₅	#121	1	1	yes	characteristic
179	C₂³×C₅	C₂²⋊Q₈	1	1	yes	characteristic
180	C₂³×C₅	C₂²⋊Q₈	1	1	yes	characteristic
181	C₂³×C₅	#123	1	1	yes	characteristic
182	C₂³×C₅	#123	1	1	yes	characteristic
183	C₂³×C₅	#127	1	1	yes	characteristic
184	C₂³×C₅	C₂×SD₁₆	1	2	yes	—
185	C₂³×C₅	#135	1	2	yes	—
186	C₂³×C₅	AGL(1,ℤ/8)	1	2	yes	—
187	C₂³×C₅	#137	1	2	yes	—
188	C₂×C₄×C₅	—	2	4	no	—
189	C₂×C₄×C₅	—	2	4	no	—
190	C₂×C₄×C₅	—	2	4	no	—
191	C₂×C₄×C₅	—	4	2	no	—
192	C₂×C₄×C₅	—	4	2	no	—
193	C₂×C₄×C₅	—	4	2	no	—
194	C₂×C₄×C₅	—	4	2	no	—
195	C₂×C₄×C₅	—	4	2	no	—
196	C₂×C₄×C₅	—	4	2	no	—
197	C₂×C₄×C₅	—	4	2	no	—
198	C₂×C₄×C₅	—	4	2	no	—
199	C₂×C₄×C₅	—	4	4	no	—
200	C₂×C₄×C₅	—	4	4	no	—
201	C₂×C₄×C₅	—	4	4	no	—
202	C₂×C₄×C₅	—	4	4	no	—
203	C₂×C₄×C₅	—	8	2	no	—
204	C₂×C₄×C₅	—	8	2	no	—
205	C₂×C₄×C₅	—	8	2	no	—
206	C₂×C₄×C₅	—	8	2	no	—
207	C₂×C₄×C₅	—	8	1	no	—
208	C₂×C₄×C₅	—	8	1	no	—
209	C₂×C₄×C₅	—	8	1	no	—
210	C₂×C₄×C₅	—	8	1	no	—
211	C₂×C₄×C₅	—	8	1	no	—
212	C₂×C₄×C₅	—	8	1	no	—
213	C₂×C₄×C₅	—	8	1	no	—
214	C₂×C₄×C₅	—	8	1	no	—
215	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
216	C₂×C₄×C₅	#117	1	1	yes	characteristic
217	C₂×C₄×C₅	#117	1	1	yes	characteristic
218	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
219	C₂×C₄×C₅	C₄×Q₈	1	1	yes	characteristic
220	C₂×C₄×C₅	C₄×Q₈	1	1	yes	characteristic
221	C₂×C₄×C₅	#121	1	1	yes	characteristic
222	C₂×C₄×C₅	C₂²⋊Q₈	1	1	yes	characteristic
223	C₂×C₄×C₅	C₂²⋊Q₈	1	1	yes	characteristic
224	C₂×C₄×C₅	C₂²⋊Q₈	1	1	yes	characteristic
225	C₂×C₄×C₅	C₂²⋊Q₈	1	1	yes	characteristic
226	C₂×C₄×C₅	#123	1	1	yes	characteristic
227	C₂×C₄×C₅	#123	1	1	yes	characteristic
228	C₂×C₄×C₅	#123	1	1	yes	characteristic
229	C₂×C₄×C₅	#123	1	1	yes	characteristic
230	C₂×C₄×C₅	#123	1	1	yes	characteristic
231	C₂×C₄×C₅	#123	1	1	yes	characteristic
232	C₂×C₄×C₅	#124	1	1	yes	characteristic
233	C₂×C₄×C₅	#124	1	1	yes	characteristic
234	C₂×C₄×C₅	#125	1	1	yes	characteristic
235	C₂×C₄×C₅	#125	1	1	yes	characteristic
236	C₂×C₄×C₅	#125	1	1	yes	characteristic
237	C₂×C₄×C₅	#125	1	1	yes	characteristic
238	C₂×C₄×C₅	#126	1	1	yes	characteristic
239	C₂×C₄×C₅	#126	1	1	yes	characteristic
240	C₂×C₄×C₅	#126	1	1	yes	characteristic
241	C₂×C₄×C₅	#126	1	1	yes	characteristic
242	C₂×C₄×C₅	C₄⋊Q₈	1	1	yes	characteristic
243	C₅×C₈	—	2	4	no	—
244	C₅×C₈	—	4	2	no	—
245	C₂³×C₄	—	2	1	no	—
246	C₂³×C₄	—	2	1	no	—
247	C₂³×C₄	—	2	1	no	—
248	C₂³×C₄	—	2	1	no	—
249	C₂³×C₄	C₅×D₄	1	2	yes	—
250	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
251	C₂²×C₈	—	2	1	no	—
252	C₂²×C₈	—	2	1	no	—
253	C₂²×C₈	—	2	1	no	—
254	C₂²×C₈	—	2	1	no	—
255	C₂²×C₈	—	2	1	no	—
256	C₂²×C₈	—	2	1	no	—
257	C₂²×C₈	—	2	1	no	—
258	C₂²×C₈	—	2	1	no	—
259	C₂²×C₈	—	2	1	no	—
260	C₂²×C₈	—	2	1	no	—
261	C₂²×C₈	C₂×C₄×C₅	1	2	yes	—
262	C₂²×C₈	C₅×D₄	1	2	yes	—
263	C₂²×C₈	C₅×D₄	1	2	yes	—
264	C₂²×C₈	C₅×D₄	1	2	yes	—
265	C₂×C₄⋊C₄	—	2	1	no	—
266	C₂×C₄⋊C₄	—	2	1	no	—
267	C₂×C₄⋊C₄	—	2	1	no	—
268	C₂×C₄⋊C₄	—	2	1	no	—
269	C₂×C₄⋊C₄	—	2	1	no	—
270	C₂×C₄⋊C₄	—	2	1	no	—
271	C₂×C₄⋊C₄	—	2	1	no	—
272	C₂×C₄⋊C₄	—	2	1	no	—
273	C₂×C₄⋊C₄	—	2	1	no	—
274	C₂×C₄⋊C₄	—	2	1	no	—
275	C₂×C₄⋊C₄	—	2	1	no	—
276	C₂×C₄⋊C₄	—	2	1	no	—
277	C₂×C₄⋊C₄	—	2	1	no	—
278	C₂×C₄⋊C₄	—	2	1	no	—
279	C₂×C₄⋊C₄	—	2	1	no	—
280	C₂×C₄⋊C₄	—	2	1	no	—
281	C₂×C₄⋊C₄	—	2	1	no	—
282	C₂×C₄⋊C₄	—	2	1	no	—
283	C₂×C₄⋊C₄	—	2	1	no	—
284	C₂×C₄⋊C₄	—	2	1	no	—
285	C₂×C₄⋊C₄	C₂×C₄×C₅	1	2	yes	—
286	C₂×C₄⋊C₄	C₂×C₄×C₅	1	2	yes	—
287	C₂×C₄⋊C₄	C₅×Q₈	1	2	yes	—
288	C₂×C₄⋊C₄	C₅×Q₈	1	2	yes	—
289	C₂×C₄²	—	2	1	no	—
290	C₂×C₄²	—	2	1	no	—
291	C₂×C₄²	—	2	1	no	—
292	C₂×C₄²	—	2	1	no	—
293	C₂×C₄²	—	2	1	no	—
294	C₂×C₄²	—	2	1	no	—
295	#106	—	2	8	no	—
296	#95	—	4	4	no	—
297	#95	—	4	4	no	—
298	C₂²×C₅	#387	1	1	yes	characteristic
299	C₂²×C₅	#387	1	1	yes	characteristic
300	C₂²×C₅	#390	1	1	yes	characteristic
301	C₂²×C₅	#397	1	1	yes	characteristic
302	C₂²×C₅	#398	1	1	yes	characteristic
303	C₂²×C₅	#399	1	1	yes	characteristic
304	C₂²×C₅	#399	1	1	yes	characteristic
305	C₂²×C₅	C₄×SD₁₆	1	2	yes	—
306	C₂²×C₅	#440	1	2	yes	—
307	C₂²×C₅	#465	1	2	yes	—
308	C₂²×C₅	#468	1	2	yes	—
309	C₂²×C₅	#475	1	2	yes	—
310	C₂²×C₅	#476	1	2	yes	—
311	C₂²×C₅	#478	1	2	yes	—
312	C₂²×C₅	#479	1	2	yes	—
313	C₂²×C₅	#481	1	2	yes	—
314	C₂²×C₅	#482	1	2	yes	—
315	C₂²×C₅	#483	1	2	yes	—
316	C₂²×C₅	#485	1	2	yes	—
317	C₂²×C₅	#492	1	1	yes	characteristic
318	C₂²×C₅	#495	1	1	yes	characteristic
319	C₂²×C₅	#496	1	1	yes	characteristic
320	C₂²×C₅	#497	1	1	yes	characteristic
321	C₄×C₅	—	4	4	no	—
322	C₄×C₅	—	8	2	no	—
323	C₄×C₅	—	8	2	no	—
324	C₄×C₅	—	8	2	no	—
325	C₄×C₅	—	8	2	no	—
326	C₄×C₅	#381	1	1	yes	characteristic
327	C₄×C₅	#387	1	1	yes	characteristic
328	C₄×C₅	#387	1	1	yes	characteristic
329	C₄×C₅	#391	1	1	yes	characteristic
330	C₄×C₅	#397	1	1	yes	characteristic
331	C₄×C₅	#398	1	1	yes	characteristic
332	C₄×C₅	#400	1	1	yes	characteristic
333	C₄×C₅	#400	1	1	yes	characteristic
334	C₂⁴	C₂×C₅×D₄	1	1	yes	characteristic
335	C₂²×C₄	—	2	2	no	—
336	C₂²×C₄	—	2	2	no	—
337	C₂²×C₄	—	2	2	no	—
338	C₂²×C₄	—	2	2	no	—
339	C₂²×C₄	—	2	2	no	—
340	C₂²×C₄	—	2	2	no	—
341	C₂²×C₄	—	2	2	no	—
342	C₂²×C₄	—	2	2	no	—
343	C₂²×C₄	—	2	2	no	—
344	C₂²×C₄	—	2	2	no	—
345	C₂²×C₄	—	4	1	no	—
346	C₂²×C₄	—	4	1	no	—
347	C₂²×C₄	—	4	1	no	—
348	C₂²×C₄	—	4	1	no	—
349	C₂²×C₄	—	4	1	no	—
350	C₂²×C₄	—	4	1	no	—
351	C₂²×C₄	—	4	1	no	—
352	C₂²×C₄	—	4	1	no	—
353	C₂²×C₄	—	4	2	no	—
354	C₂²×C₄	—	4	2	no	—
355	C₂²×C₄	—	4	2	no	—
356	C₂²×C₄	—	4	2	no	—
357	C₂²×C₄	—	4	2	no	—
358	C₂²×C₄	—	4	2	no	—
359	C₂²×C₄	—	4	2	no	—
360	C₂²×C₄	—	4	2	no	—
361	C₂²×C₄	C₅×SD₁₆	1	4	yes	—
362	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
363	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
364	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
365	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
366	C₂²×C₄	C₂×C₅×Q₈	1	1	yes	characteristic
367	C₂²×C₄	C₂×C₅×Q₈	1	1	yes	characteristic
368	C₂²×C₄	C₅×#41	1	1	yes	characteristic
369	C₂²×C₄	C₅×#41	1	1	yes	characteristic
370	C₂²×C₄	C₅×#41	1	1	yes	characteristic
371	C₂²×C₄	C₅×#41	1	1	yes	characteristic
372	C₂²×C₄	C₅×#41	1	1	yes	characteristic
373	C₂²×C₄	C₅×#41	1	1	yes	characteristic
374	C₂²×C₄	C₅×#41	1	1	yes	characteristic
375	C₂²×C₄	C₅×#41	1	1	yes	characteristic
376	C₂×C₈	—	2	2	no	—
377	C₂×C₈	—	2	2	no	—
378	C₂×C₈	—	2	2	no	—
379	C₂×C₈	—	2	2	no	—
380	C₂×C₈	—	2	2	no	—
381	C₂×C₈	—	2	2	no	—
382	C₂×C₈	—	2	2	no	—
383	C₂×C₈	—	2	2	no	—
384	C₂×C₈	—	2	2	no	—
385	C₂×C₈	—	4	1	no	—
386	C₂×C₈	—	4	1	no	—
387	C₂×C₈	—	4	1	no	—
388	C₂×C₈	—	4	1	no	—
389	C₂×C₈	C₅×C₂²⋊C₄	1	4	yes	—
390	C₄⋊C₄	—	2	2	no	—
391	C₄⋊C₄	—	2	2	no	—
392	C₄⋊C₄	—	2	2	no	—
393	C₄⋊C₄	—	2	2	no	—
394	C₄⋊C₄	—	2	2	no	—
395	C₄⋊C₄	—	2	2	no	—
396	C₄⋊C₄	—	2	2	no	—
397	C₄⋊C₄	—	2	2	no	—
398	C₄⋊C₄	—	4	1	no	—
399	C₄⋊C₄	—	4	1	no	—
400	C₄⋊C₄	—	4	1	no	—
401	C₄⋊C₄	—	4	1	no	—
402	C₄⋊C₄	—	4	1	no	—
403	C₄⋊C₄	—	4	1	no	—
404	C₄⋊C₄	—	4	1	no	—
405	C₄⋊C₄	—	4	1	no	—
406	C₄²	—	4	1	no	—
407	C₄²	—	4	1	no	—
408	C₄²	—	4	1	no	—
409	C₄²	—	4	1	no	—
410	C₂×C₅	#1445	1	1	yes	characteristic
411	C₂×C₅	#1919	1	2	yes	—
412	C₂×C₅	#1920	1	2	yes	—
413	C₂×C₅	#1968	1	1	yes	characteristic
414	C₂×C₅	#1973	1	1	yes	characteristic
415	C₂×C₅	#2077	1	2	yes	—
416	C₂×C₅	#2088	1	2	yes	—
417	C₂×C₅	#2092	1	1	yes	characteristic
418	C₂×C₅	#2094	1	1	yes	characteristic
419	C₂×C₅	#2096	1	1	yes	characteristic
420	C₂×C₅	#2097	1	1	yes	characteristic
421	C₂³	C₄×C₅×D₄	1	1	yes	characteristic
422	C₂³	C₅×#121	1	1	yes	characteristic
423	C₂³	C₅×C₂²⋊Q₈	1	1	yes	characteristic
424	C₂³	C₅×C₂²⋊Q₈	1	1	yes	characteristic
425	C₂³	C₅×#123	1	1	yes	characteristic
426	C₂³	C₅×#123	1	1	yes	characteristic
427	C₂³	C₅×#127	1	1	yes	characteristic
428	C₂³	C₂×C₅×SD₁₆	1	2	yes	—
429	C₂³	C₅×#135	1	2	yes	—
430	C₂³	C₅×AGL(1,ℤ/8)	1	2	yes	—
431	C₂³	C₅×#137	1	2	yes	—
432	C₂×C₄	—	2	4	no	—
433	C₂×C₄	—	2	4	no	—
434	C₂×C₄	—	2	4	no	—
435	C₂×C₄	—	4	2	no	—
436	C₂×C₄	—	4	2	no	—
437	C₂×C₄	—	4	2	no	—
438	C₂×C₄	—	4	2	no	—
439	C₂×C₄	—	4	2	no	—
440	C₂×C₄	—	4	2	no	—
441	C₂×C₄	—	4	2	no	—
442	C₂×C₄	—	4	2	no	—
443	C₂×C₄	—	4	4	no	—
444	C₂×C₄	—	4	4	no	—
445	C₂×C₄	—	4	4	no	—
446	C₂×C₄	—	4	4	no	—
447	C₂×C₄	—	8	2	no	—
448	C₂×C₄	—	8	2	no	—
449	C₂×C₄	—	8	2	no	—
450	C₂×C₄	—	8	2	no	—
451	C₂×C₄	—	8	1	no	—
452	C₂×C₄	—	8	1	no	—
453	C₂×C₄	—	8	1	no	—
454	C₂×C₄	—	8	1	no	—
455	C₂×C₄	—	8	1	no	—
456	C₂×C₄	—	8	1	no	—
457	C₂×C₄	—	8	1	no	—
458	C₂×C₄	—	8	1	no	—
459	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
460	C₂×C₄	C₅×#117	1	1	yes	characteristic
461	C₂×C₄	C₅×#117	1	1	yes	characteristic
462	C₂×C₄	C₄×C₅×D₄	1	1	yes	characteristic
463	C₂×C₄	C₄×C₅×Q₈	1	1	yes	characteristic
464	C₂×C₄	C₄×C₅×Q₈	1	1	yes	characteristic
465	C₂×C₄	C₅×#121	1	1	yes	characteristic
466	C₂×C₄	C₅×C₂²⋊Q₈	1	1	yes	characteristic
467	C₂×C₄	C₅×C₂²⋊Q₈	1	1	yes	characteristic
468	C₂×C₄	C₅×C₂²⋊Q₈	1	1	yes	characteristic
469	C₂×C₄	C₅×C₂²⋊Q₈	1	1	yes	characteristic
470	C₂×C₄	C₅×#123	1	1	yes	characteristic
471	C₂×C₄	C₅×#123	1	1	yes	characteristic
472	C₂×C₄	C₅×#123	1	1	yes	characteristic
473	C₂×C₄	C₅×#123	1	1	yes	characteristic
474	C₂×C₄	C₅×#123	1	1	yes	characteristic
475	C₂×C₄	C₅×#123	1	1	yes	characteristic
476	C₂×C₄	C₅×#124	1	1	yes	characteristic
477	C₂×C₄	C₅×#124	1	1	yes	characteristic
478	C₂×C₄	C₅×#125	1	1	yes	characteristic
479	C₂×C₄	C₅×#125	1	1	yes	characteristic
480	C₂×C₄	C₅×#125	1	1	yes	characteristic
481	C₂×C₄	C₅×#125	1	1	yes	characteristic
482	C₂×C₄	C₅×#126	1	1	yes	characteristic
483	C₂×C₄	C₅×#126	1	1	yes	characteristic
484	C₂×C₄	C₅×#126	1	1	yes	characteristic
485	C₂×C₄	C₅×#126	1	1	yes	characteristic
486	C₂×C₄	C₅×C₄⋊Q₈	1	1	yes	characteristic
487	C₈	—	2	4	no	—
488	C₈	—	4	2	no	—
489	C₅	#11378	1	1	yes	characteristic, direct product factor, Sylow
490	C₂²	C₅×#387	1	1	yes	characteristic
491	C₂²	C₅×#387	1	1	yes	characteristic
492	C₂²	C₅×#390	1	1	yes	characteristic
493	C₂²	C₅×#397	1	1	yes	characteristic
494	C₂²	C₅×#398	1	1	yes	characteristic
495	C₂²	C₅×#399	1	1	yes	characteristic
496	C₂²	C₅×#399	1	1	yes	characteristic
497	C₂²	C₄×C₅×SD₁₆	1	2	yes	—
498	C₂²	C₅×#440	1	2	yes	—
499	C₂²	C₅×#465	1	2	yes	—
500	C₂²	C₅×#468	1	2	yes	—
501	C₂²	C₅×#475	1	2	yes	—
502	C₂²	C₅×#476	1	2	yes	—
503	C₂²	C₅×#478	1	2	yes	—
504	C₂²	C₅×#479	1	2	yes	—
505	C₂²	C₅×#481	1	2	yes	—
506	C₂²	C₅×#482	1	2	yes	—
507	C₂²	C₅×#483	1	2	yes	—
508	C₂²	C₅×#485	1	2	yes	—
509	C₂²	C₅×#492	1	1	yes	characteristic
510	C₂²	C₅×#495	1	1	yes	characteristic
511	C₂²	C₅×#496	1	1	yes	characteristic
512	C₂²	C₅×#497	1	1	yes	characteristic
513	C₄	—	4	4	no	—
514	C₄	—	8	2	no	—
515	C₄	—	8	2	no	—
516	C₄	—	8	2	no	—
517	C₄	—	8	2	no	—
518	C₄	C₅×#381	1	1	yes	characteristic
519	C₄	C₅×#387	1	1	yes	characteristic
520	C₄	C₅×#387	1	1	yes	characteristic
521	C₄	C₅×#391	1	1	yes	characteristic
522	C₄	C₅×#397	1	1	yes	characteristic
523	C₄	C₅×#398	1	1	yes	characteristic
524	C₄	C₅×#400	1	1	yes	characteristic
525	C₄	C₅×#400	1	1	yes	characteristic
526	C₂	C₅×#1445	1	1	yes	characteristic
527	C₂	C₅×#1919	1	2	yes	—
528	C₂	C₅×#1920	1	2	yes	—
529	C₂	C₅×#1968	1	1	yes	characteristic
530	C₂	C₅×#1973	1	1	yes	characteristic
531	C₂	C₅×#2077	1	2	yes	—
532	C₂	C₅×#2088	1	2	yes	—
533	C₂	C₅×#2092	1	1	yes	characteristic
534	C₂	C₅×#2094	1	1	yes	characteristic
535	C₂	C₅×#2096	1	1	yes	characteristic
536	C₂	C₅×#2097	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂⁴×C₅	C₂×D₄
commutator	C₂²×C₄	C₂²×C₄×C₅
Frattini, cosocle	C₂³×C₄	C₂³×C₅
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₅ ◁ C₂²×C₄²×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
17. C₂×C₅×#106	C₄	semidirect
24. #11378	C₅	direct (N × H)
170. C₂×#106	C₄×C₅	semidirect
489. C₅	#11378	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂²×C₅×#106	2
C₂×C₅×#340	2
C₂×C₅×#336	2
C₅×C₄⋊#95	2
#11378	5

Subgroups — C5×#11378 #11934098

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#11378 #11934098