Subgroups — C₅×#11325 #11934045

Order 1280.

886 conjugacy classes of subgroups.

The subgroup lattice has 548 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₅×#107	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₅×#106	C₂	1	1	yes	maximal, characteristic
3	C₂×C₅×#382	C₂	1	1	yes	maximal, characteristic
4	C₂×C₅×#340	C₂	1	1	yes	maximal, characteristic
5	C₂×C₅×#340	C₂	1	1	yes	maximal, characteristic
6	C₂×C₅×#336	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×#107	—	2	2	no	—
16	C₂×C₅×#107	—	2	2	no	—
17	C₂×C₅×#107	—	2	2	no	—
18	C₂×C₅×#106	—	2	2	no	—
19	C₂×C₅×#106	—	2	2	no	—
20	C₂×C₅×#106	—	2	2	no	—
21	C₅×#382	—	2	2	no	—
22	C₅×#382	—	2	2	no	—
23	C₂×C₅×#95	—	2	2	no	—
24	C₂×C₅×#95	—	2	2	no	—
25	C₅×#340	—	2	2	no	—
26	C₅×#340	—	2	2	no	—
27	C₅×#336	C₄	1	4	yes	complemented
28	#11325	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
29	C₂³×C₄×C₅	—	2	1	no	—
30	C₂³×C₄×C₅	—	2	1	no	—
31	C₂³×C₄×C₅	—	2	1	no	—
32	C₂³×C₄×C₅	—	2	1	no	—
33	C₂³×C₄×C₅	D₄	1	2	yes	—
34	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
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	—	2	1	no	—
42	C₂²×C₅×C₈	—	2	1	no	—
43	C₂²×C₅×C₈	C₂×C₄	1	2	yes	—
44	C₂²×C₅×C₈	C₂×C₄	1	2	yes	—
45	C₂²×C₅×C₈	D₄	1	2	yes	—
46	C₂²×C₅×C₈	D₄	1	2	yes	—
47	C₂²×C₅×C₈	Q₈	1	2	yes	—
48	C₂²×C₅×C₈	Q₈	1	2	yes	—
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	—	2	1	no	—
66	C₂×C₅×C₄⋊C₄	—	2	1	no	—
67	C₂×C₅×C₄⋊C₄	—	2	1	no	—
68	C₂×C₅×C₄⋊C₄	—	2	1	no	—
69	C₂×C₅×C₄⋊C₄	D₄	1	2	yes	—
70	C₂×C₅×C₄⋊C₄	D₄	1	2	yes	—
71	C₂×C₅×C₄⋊C₄	D₄	1	2	yes	—
72	C₂×C₅×C₄⋊C₄	Q₈	1	2	yes	—
73	C₂×C₄²×C₅	—	2	1	no	—
74	C₂×C₄²×C₅	—	2	1	no	—
75	C₂×C₄²×C₅	—	2	1	no	—
76	C₂×C₄²×C₅	—	2	1	no	—
77	C₂×C₄²×C₅	C₂×C₄	1	2	yes	—
78	C₂×C₄²×C₅	Q₈	1	2	yes	—
79	C₅×#107	—	2	8	no	—
80	C₅×#106	—	2	8	no	—
81	C₅×#95	—	2	8	no	—
82	C₅×#95	—	4	4	no	—
83	C₂²×#107	C₂×C₅	1	1	yes	characteristic
84	C₂²×#106	C₂×C₅	1	1	yes	characteristic
85	C₂×#382	C₂×C₅	1	1	yes	characteristic
86	C₂×#340	C₂×C₅	1	1	yes	characteristic
87	C₂×#340	C₂×C₅	1	1	yes	characteristic
88	C₂×#336	C₂×C₅	1	1	yes	characteristic
89	C₄⋊#95	C₂×C₅	1	1	yes	characteristic
90	C₂⁴×C₅	C₂×D₄	1	1	yes	characteristic
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	—	2	2	no	—
97	C₂²×C₄×C₅	—	2	2	no	—
98	C₂²×C₄×C₅	—	2	2	no	—
99	C₂²×C₄×C₅	—	2	2	no	—
100	C₂²×C₄×C₅	—	2	2	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	1	no	—
105	C₂²×C₄×C₅	—	4	1	no	—
106	C₂²×C₄×C₅	—	4	1	no	—
107	C₂²×C₄×C₅	—	4	1	no	—
108	C₂²×C₄×C₅	—	4	1	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	—	4	2	no	—
113	C₂²×C₄×C₅	—	4	2	no	—
114	C₂²×C₄×C₅	—	4	2	no	—
115	C₂²×C₄×C₅	—	4	2	no	—
116	C₂²×C₄×C₅	—	4	2	no	—
117	C₂²×C₄×C₅	C₄⋊C₄	1	4	yes	—
118	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
119	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
120	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
121	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
122	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
123	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
124	C₂²×C₄×C₅	C₂×Q₈	1	1	yes	characteristic
125	C₂²×C₄×C₅	C₂×Q₈	1	1	yes	characteristic
126	C₂²×C₄×C₅	C₂×Q₈	1	1	yes	characteristic
127	C₂²×C₄×C₅	C₂×Q₈	1	1	yes	characteristic
128	C₂²×C₄×C₅	#41	1	1	yes	characteristic
129	C₂²×C₄×C₅	#41	1	1	yes	characteristic
130	C₂²×C₄×C₅	#41	1	1	yes	characteristic
131	C₂²×C₄×C₅	#41	1	1	yes	characteristic
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	—	2	2	no	—
137	C₂×C₅×C₈	—	2	2	no	—
138	C₂×C₅×C₈	—	2	2	no	—
139	C₂×C₅×C₈	—	2	2	no	—
140	C₂×C₅×C₈	—	2	2	no	—
141	C₂×C₅×C₈	—	2	2	no	—
142	C₂×C₅×C₈	—	2	2	no	—
143	C₂×C₅×C₈	—	2	2	no	—
144	C₂×C₅×C₈	C₄⋊C₄	1	4	yes	—
145	C₂×C₅×C₈	C₄⋊C₄	1	4	yes	—
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	—	2	2	no	—
150	C₅×C₄⋊C₄	—	2	2	no	—
151	C₅×C₄⋊C₄	—	2	2	no	—
152	C₅×C₄⋊C₄	—	2	2	no	—
153	C₅×C₄⋊C₄	—	2	2	no	—
154	C₅×C₄⋊C₄	—	4	1	no	—
155	C₅×C₄⋊C₄	—	4	1	no	—
156	C₅×C₄⋊C₄	—	4	1	no	—
157	C₅×C₄⋊C₄	—	4	1	no	—
158	C₅×C₄⋊C₄	—	4	1	no	—
159	C₅×C₄⋊C₄	—	4	1	no	—
160	C₅×C₄⋊C₄	—	4	1	no	—
161	C₅×C₄⋊C₄	—	4	1	no	—
162	C₄²×C₅	—	2	2	no	—
163	C₄²×C₅	—	2	2	no	—
164	C₄²×C₅	—	2	2	no	—
165	C₄²×C₅	—	2	2	no	—
166	C₂³×C₈	C₂²×C₅	1	1	yes	characteristic
167	C₂³×C₈	C₂²×C₅	1	1	yes	characteristic
168	C₂²×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
169	C₂²×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
170	C₂²×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
171	C₂²×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
172	C₂²×C₄²	C₂²×C₅	1	1	yes	characteristic
173	C₂×#107	—	2	2	no	—
174	C₂×#107	—	2	2	no	—
175	C₂×#107	—	2	2	no	—
176	C₂×#106	—	2	2	no	—
177	C₂×#106	—	2	2	no	—
178	C₂×#106	—	2	2	no	—
179	#382	—	2	2	no	—
180	#382	—	2	2	no	—
181	C₂×#95	—	2	2	no	—
182	C₂×#95	—	2	2	no	—
183	#340	—	2	2	no	—
184	#340	—	2	2	no	—
185	#336	C₄×C₅	1	4	yes	complemented
186	C₂³×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
187	C₂³×C₅	#120	1	1	yes	characteristic
188	C₂³×C₅	#121	1	1	yes	characteristic
189	C₂³×C₅	C₂²⋊Q₈	1	1	yes	characteristic
190	C₂³×C₅	#123	1	1	yes	characteristic
191	C₂³×C₅	#127	1	1	yes	characteristic
192	C₂³×C₅	C₄⋊Q₈	1	1	yes	characteristic
193	C₂³×C₅	#135	1	2	yes	—
194	C₂³×C₅	#135	1	2	yes	—
195	C₂³×C₅	AGL(1,ℤ/8)	1	2	yes	—
196	C₂³×C₅	#137	1	2	yes	—
197	C₂×C₄×C₅	—	2	4	no	—
198	C₂×C₄×C₅	—	2	4	no	—
199	C₂×C₄×C₅	—	2	4	no	—
200	C₂×C₄×C₅	—	4	2	no	—
201	C₂×C₄×C₅	—	4	2	no	—
202	C₂×C₄×C₅	—	4	2	no	—
203	C₂×C₄×C₅	—	4	2	no	—
204	C₂×C₄×C₅	—	4	2	no	—
205	C₂×C₄×C₅	—	4	2	no	—
206	C₂×C₄×C₅	—	4	2	no	—
207	C₂×C₄×C₅	—	4	2	no	—
208	C₂×C₄×C₅	—	4	4	no	—
209	C₂×C₄×C₅	—	4	4	no	—
210	C₂×C₄×C₅	—	4	4	no	—
211	C₂×C₄×C₅	—	4	4	no	—
212	C₂×C₄×C₅	—	8	2	no	—
213	C₂×C₄×C₅	—	8	2	no	—
214	C₂×C₄×C₅	—	8	2	no	—
215	C₂×C₄×C₅	—	8	2	no	—
216	C₂×C₄×C₅	—	8	1	no	—
217	C₂×C₄×C₅	—	8	1	no	—
218	C₂×C₄×C₅	—	8	1	no	—
219	C₂×C₄×C₅	—	8	1	no	—
220	C₂×C₄×C₅	—	8	1	no	—
221	C₂×C₄×C₅	—	8	1	no	—
222	C₂×C₄×C₅	—	8	1	no	—
223	C₂×C₄×C₅	—	8	1	no	—
224	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
225	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
226	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
227	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
228	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
229	C₂×C₄×C₅	C₄×Q₈	1	1	yes	characteristic
230	C₂×C₄×C₅	#120	1	1	yes	characteristic
231	C₂×C₄×C₅	#120	1	1	yes	characteristic
232	C₂×C₄×C₅	#121	1	1	yes	characteristic
233	C₂×C₄×C₅	#121	1	1	yes	characteristic
234	C₂×C₄×C₅	C₂²⋊Q₈	1	1	yes	characteristic
235	C₂×C₄×C₅	C₂²⋊Q₈	1	1	yes	characteristic
236	C₂×C₄×C₅	C₂²⋊Q₈	1	1	yes	characteristic
237	C₂×C₄×C₅	C₂²⋊Q₈	1	1	yes	characteristic
238	C₂×C₄×C₅	C₂²⋊Q₈	1	1	yes	characteristic
239	C₂×C₄×C₅	C₂²⋊Q₈	1	1	yes	characteristic
240	C₂×C₄×C₅	C₂²⋊Q₈	1	1	yes	characteristic
241	C₂×C₄×C₅	C₂²⋊Q₈	1	1	yes	characteristic
242	C₂×C₄×C₅	#123	1	1	yes	characteristic
243	C₂×C₄×C₅	#123	1	1	yes	characteristic
244	C₂×C₄×C₅	#125	1	1	yes	characteristic
245	C₂×C₄×C₅	#125	1	1	yes	characteristic
246	C₂×C₄×C₅	#125	1	1	yes	characteristic
247	C₂×C₄×C₅	C₄⋊Q₈	1	1	yes	characteristic
248	C₂×C₄×C₅	C₄⋊Q₈	1	1	yes	characteristic
249	C₂×C₄×C₅	C₄⋊Q₈	1	1	yes	characteristic
250	C₂×C₄×C₅	C₄⋊Q₈	1	1	yes	characteristic
251	C₂×C₄×C₅	C₄⋊Q₈	1	1	yes	characteristic
252	C₅×C₈	—	2	4	no	—
253	C₅×C₈	—	2	4	no	—
254	C₂³×C₄	—	2	1	no	—
255	C₂³×C₄	—	2	1	no	—
256	C₂³×C₄	—	2	1	no	—
257	C₂³×C₄	—	2	1	no	—
258	C₂³×C₄	C₅×D₄	1	2	yes	—
259	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
260	C₂²×C₈	—	2	1	no	—
261	C₂²×C₈	—	2	1	no	—
262	C₂²×C₈	—	2	1	no	—
263	C₂²×C₈	—	2	1	no	—
264	C₂²×C₈	—	2	1	no	—
265	C₂²×C₈	—	2	1	no	—
266	C₂²×C₈	—	2	1	no	—
267	C₂²×C₈	—	2	1	no	—
268	C₂²×C₈	C₂×C₄×C₅	1	2	yes	—
269	C₂²×C₈	C₂×C₄×C₅	1	2	yes	—
270	C₂²×C₈	C₅×D₄	1	2	yes	—
271	C₂²×C₈	C₅×D₄	1	2	yes	—
272	C₂²×C₈	C₅×Q₈	1	2	yes	—
273	C₂²×C₈	C₅×Q₈	1	2	yes	—
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	—	2	1	no	—
286	C₂×C₄⋊C₄	—	2	1	no	—
287	C₂×C₄⋊C₄	—	2	1	no	—
288	C₂×C₄⋊C₄	—	2	1	no	—
289	C₂×C₄⋊C₄	—	2	1	no	—
290	C₂×C₄⋊C₄	—	2	1	no	—
291	C₂×C₄⋊C₄	—	2	1	no	—
292	C₂×C₄⋊C₄	—	2	1	no	—
293	C₂×C₄⋊C₄	—	2	1	no	—
294	C₂×C₄⋊C₄	C₅×D₄	1	2	yes	—
295	C₂×C₄⋊C₄	C₅×D₄	1	2	yes	—
296	C₂×C₄⋊C₄	C₅×D₄	1	2	yes	—
297	C₂×C₄⋊C₄	C₅×Q₈	1	2	yes	—
298	C₂×C₄²	—	2	1	no	—
299	C₂×C₄²	—	2	1	no	—
300	C₂×C₄²	—	2	1	no	—
301	C₂×C₄²	—	2	1	no	—
302	C₂×C₄²	C₂×C₄×C₅	1	2	yes	—
303	C₂×C₄²	C₅×Q₈	1	2	yes	—
304	#107	—	2	8	no	—
305	#106	—	2	8	no	—
306	#95	—	2	8	no	—
307	#95	—	4	4	no	—
308	C₂²×C₅	#384	1	1	yes	characteristic
309	C₂²×C₅	#385	1	1	yes	characteristic
310	C₂²×C₅	#389	1	1	yes	characteristic
311	C₂²×C₅	#392	1	1	yes	characteristic
312	C₂²×C₅	#395	1	1	yes	characteristic
313	C₂²×C₅	#398	1	1	yes	characteristic
314	C₂²×C₅	#399	1	1	yes	characteristic
315	C₂²×C₅	#427	1	2	yes	—
316	C₂²×C₅	#428	1	2	yes	—
317	C₂²×C₅	#449	1	2	yes	—
318	C₂²×C₅	#452	1	2	yes	—
319	C₂²×C₅	#463	1	2	yes	—
320	C₂²×C₅	#464	1	2	yes	—
321	C₂²×C₅	#478	1	2	yes	—
322	C₂²×C₅	#479	1	2	yes	—
323	C₂²×C₅	#482	1	2	yes	—
324	C₂²×C₅	#485	1	2	yes	—
325	C₂²×C₅	#495	1	1	yes	characteristic
326	C₂²×C₅	#495	1	1	yes	characteristic
327	C₂²×C₅	#496	1	1	yes	characteristic
328	C₂²×C₅	#497	1	1	yes	characteristic
329	C₂²×C₅	#499	1	2	yes	—
330	C₂²×C₅	#501	1	2	yes	—
331	C₄×C₅	—	4	4	no	—
332	C₄×C₅	—	8	2	no	—
333	C₄×C₅	—	8	2	no	—
334	C₄×C₅	—	8	2	no	—
335	C₄×C₅	—	8	2	no	—
336	C₄×C₅	#385	1	1	yes	characteristic
337	C₄×C₅	#385	1	1	yes	characteristic
338	C₄×C₅	#389	1	1	yes	characteristic
339	C₄×C₅	#389	1	1	yes	characteristic
340	C₄×C₅	#395	1	1	yes	characteristic
341	C₄×C₅	#395	1	1	yes	characteristic
342	C₄×C₅	#398	1	1	yes	characteristic
343	C₄×C₅	#398	1	1	yes	characteristic
344	C₂⁴	C₂×C₅×D₄	1	1	yes	characteristic
345	C₂²×C₄	—	2	2	no	—
346	C₂²×C₄	—	2	2	no	—
347	C₂²×C₄	—	2	2	no	—
348	C₂²×C₄	—	2	2	no	—
349	C₂²×C₄	—	2	2	no	—
350	C₂²×C₄	—	2	2	no	—
351	C₂²×C₄	—	2	2	no	—
352	C₂²×C₄	—	2	2	no	—
353	C₂²×C₄	—	2	2	no	—
354	C₂²×C₄	—	2	2	no	—
355	C₂²×C₄	—	4	1	no	—
356	C₂²×C₄	—	4	1	no	—
357	C₂²×C₄	—	4	1	no	—
358	C₂²×C₄	—	4	1	no	—
359	C₂²×C₄	—	4	1	no	—
360	C₂²×C₄	—	4	1	no	—
361	C₂²×C₄	—	4	1	no	—
362	C₂²×C₄	—	4	1	no	—
363	C₂²×C₄	—	4	2	no	—
364	C₂²×C₄	—	4	2	no	—
365	C₂²×C₄	—	4	2	no	—
366	C₂²×C₄	—	4	2	no	—
367	C₂²×C₄	—	4	2	no	—
368	C₂²×C₄	—	4	2	no	—
369	C₂²×C₄	—	4	2	no	—
370	C₂²×C₄	—	4	2	no	—
371	C₂²×C₄	C₅×C₄⋊C₄	1	4	yes	—
372	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
373	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
374	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
375	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
376	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
377	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
378	C₂²×C₄	C₂×C₅×Q₈	1	1	yes	characteristic
379	C₂²×C₄	C₂×C₅×Q₈	1	1	yes	characteristic
380	C₂²×C₄	C₂×C₅×Q₈	1	1	yes	characteristic
381	C₂²×C₄	C₂×C₅×Q₈	1	1	yes	characteristic
382	C₂²×C₄	C₅×#41	1	1	yes	characteristic
383	C₂²×C₄	C₅×#41	1	1	yes	characteristic
384	C₂²×C₄	C₅×#41	1	1	yes	characteristic
385	C₂²×C₄	C₅×#41	1	1	yes	characteristic
386	C₂×C₈	—	2	2	no	—
387	C₂×C₈	—	2	2	no	—
388	C₂×C₈	—	2	2	no	—
389	C₂×C₈	—	2	2	no	—
390	C₂×C₈	—	2	2	no	—
391	C₂×C₈	—	2	2	no	—
392	C₂×C₈	—	2	2	no	—
393	C₂×C₈	—	2	2	no	—
394	C₂×C₈	—	2	2	no	—
395	C₂×C₈	—	2	2	no	—
396	C₂×C₈	—	2	2	no	—
397	C₂×C₈	—	2	2	no	—
398	C₂×C₈	C₅×C₄⋊C₄	1	4	yes	—
399	C₂×C₈	C₅×C₄⋊C₄	1	4	yes	—
400	C₄⋊C₄	—	2	2	no	—
401	C₄⋊C₄	—	2	2	no	—
402	C₄⋊C₄	—	2	2	no	—
403	C₄⋊C₄	—	2	2	no	—
404	C₄⋊C₄	—	2	2	no	—
405	C₄⋊C₄	—	2	2	no	—
406	C₄⋊C₄	—	2	2	no	—
407	C₄⋊C₄	—	2	2	no	—
408	C₄⋊C₄	—	4	1	no	—
409	C₄⋊C₄	—	4	1	no	—
410	C₄⋊C₄	—	4	1	no	—
411	C₄⋊C₄	—	4	1	no	—
412	C₄⋊C₄	—	4	1	no	—
413	C₄⋊C₄	—	4	1	no	—
414	C₄⋊C₄	—	4	1	no	—
415	C₄⋊C₄	—	4	1	no	—
416	C₄²	—	2	2	no	—
417	C₄²	—	2	2	no	—
418	C₄²	—	2	2	no	—
419	C₄²	—	2	2	no	—
420	C₂×C₅	#1444	1	1	yes	characteristic
421	C₂×C₅	#1846	1	1	yes	characteristic
422	C₂×C₅	#1847	1	1	yes	characteristic
423	C₂×C₅	#1854	1	2	yes	—
424	C₂×C₅	#1949	1	2	yes	—
425	C₂×C₅	#2012	1	1	yes	characteristic
426	C₂×C₅	#2015	1	1	yes	characteristic
427	C₂×C₅	#2059	1	2	yes	—
428	C₂×C₅	#2085	1	2	yes	—
429	C₂×C₅	#2092	1	1	yes	characteristic
430	C₂×C₅	#2097	1	1	yes	characteristic
431	C₂³	C₂×C₅×C₄⋊C₄	1	1	yes	characteristic
432	C₂³	C₅×#120	1	1	yes	characteristic
433	C₂³	C₅×#121	1	1	yes	characteristic
434	C₂³	C₅×C₂²⋊Q₈	1	1	yes	characteristic
435	C₂³	C₅×#123	1	1	yes	characteristic
436	C₂³	C₅×#127	1	1	yes	characteristic
437	C₂³	C₅×C₄⋊Q₈	1	1	yes	characteristic
438	C₂³	C₅×#135	1	2	yes	—
439	C₂³	C₅×#135	1	2	yes	—
440	C₂³	C₅×AGL(1,ℤ/8)	1	2	yes	—
441	C₂³	C₅×#137	1	2	yes	—
442	C₂×C₄	—	2	4	no	—
443	C₂×C₄	—	2	4	no	—
444	C₂×C₄	—	2	4	no	—
445	C₂×C₄	—	4	2	no	—
446	C₂×C₄	—	4	2	no	—
447	C₂×C₄	—	4	2	no	—
448	C₂×C₄	—	4	2	no	—
449	C₂×C₄	—	4	2	no	—
450	C₂×C₄	—	4	2	no	—
451	C₂×C₄	—	4	2	no	—
452	C₂×C₄	—	4	2	no	—
453	C₂×C₄	—	4	4	no	—
454	C₂×C₄	—	4	4	no	—
455	C₂×C₄	—	4	4	no	—
456	C₂×C₄	—	4	4	no	—
457	C₂×C₄	—	8	2	no	—
458	C₂×C₄	—	8	2	no	—
459	C₂×C₄	—	8	2	no	—
460	C₂×C₄	—	8	2	no	—
461	C₂×C₄	—	8	1	no	—
462	C₂×C₄	—	8	1	no	—
463	C₂×C₄	—	8	1	no	—
464	C₂×C₄	—	8	1	no	—
465	C₂×C₄	—	8	1	no	—
466	C₂×C₄	—	8	1	no	—
467	C₂×C₄	—	8	1	no	—
468	C₂×C₄	—	8	1	no	—
469	C₂×C₄	C₂×C₅×C₄⋊C₄	1	1	yes	characteristic
470	C₂×C₄	C₂×C₅×C₄⋊C₄	1	1	yes	characteristic
471	C₂×C₄	C₄×C₅×D₄	1	1	yes	characteristic
472	C₂×C₄	C₄×C₅×D₄	1	1	yes	characteristic
473	C₂×C₄	C₄×C₅×D₄	1	1	yes	characteristic
474	C₂×C₄	C₄×C₅×Q₈	1	1	yes	characteristic
475	C₂×C₄	C₅×#120	1	1	yes	characteristic
476	C₂×C₄	C₅×#120	1	1	yes	characteristic
477	C₂×C₄	C₅×#121	1	1	yes	characteristic
478	C₂×C₄	C₅×#121	1	1	yes	characteristic
479	C₂×C₄	C₅×C₂²⋊Q₈	1	1	yes	characteristic
480	C₂×C₄	C₅×C₂²⋊Q₈	1	1	yes	characteristic
481	C₂×C₄	C₅×C₂²⋊Q₈	1	1	yes	characteristic
482	C₂×C₄	C₅×C₂²⋊Q₈	1	1	yes	characteristic
483	C₂×C₄	C₅×C₂²⋊Q₈	1	1	yes	characteristic
484	C₂×C₄	C₅×C₂²⋊Q₈	1	1	yes	characteristic
485	C₂×C₄	C₅×C₂²⋊Q₈	1	1	yes	characteristic
486	C₂×C₄	C₅×C₂²⋊Q₈	1	1	yes	characteristic
487	C₂×C₄	C₅×#123	1	1	yes	characteristic
488	C₂×C₄	C₅×#123	1	1	yes	characteristic
489	C₂×C₄	C₅×#125	1	1	yes	characteristic
490	C₂×C₄	C₅×#125	1	1	yes	characteristic
491	C₂×C₄	C₅×#125	1	1	yes	characteristic
492	C₂×C₄	C₅×C₄⋊Q₈	1	1	yes	characteristic
493	C₂×C₄	C₅×C₄⋊Q₈	1	1	yes	characteristic
494	C₂×C₄	C₅×C₄⋊Q₈	1	1	yes	characteristic
495	C₂×C₄	C₅×C₄⋊Q₈	1	1	yes	characteristic
496	C₂×C₄	C₅×C₄⋊Q₈	1	1	yes	characteristic
497	C₈	—	2	4	no	—
498	C₈	—	2	4	no	—
499	C₅	#11325	1	1	yes	characteristic, direct product factor, Sylow
500	C₂²	C₅×#384	1	1	yes	characteristic
501	C₂²	C₅×#385	1	1	yes	characteristic
502	C₂²	C₅×#389	1	1	yes	characteristic
503	C₂²	C₅×#392	1	1	yes	characteristic
504	C₂²	C₅×#395	1	1	yes	characteristic
505	C₂²	C₅×#398	1	1	yes	characteristic
506	C₂²	C₅×#399	1	1	yes	characteristic
507	C₂²	C₅×#427	1	2	yes	—
508	C₂²	C₅×#428	1	2	yes	—
509	C₂²	C₅×#449	1	2	yes	—
510	C₂²	C₅×#452	1	2	yes	—
511	C₂²	C₅×#463	1	2	yes	—
512	C₂²	C₅×#464	1	2	yes	—
513	C₂²	C₅×#478	1	2	yes	—
514	C₂²	C₅×#479	1	2	yes	—
515	C₂²	C₅×#482	1	2	yes	—
516	C₂²	C₅×#485	1	2	yes	—
517	C₂²	C₅×#495	1	1	yes	characteristic
518	C₂²	C₅×#495	1	1	yes	characteristic
519	C₂²	C₅×#496	1	1	yes	characteristic
520	C₂²	C₅×#497	1	1	yes	characteristic
521	C₂²	C₅×#499	1	2	yes	—
522	C₂²	C₅×#501	1	2	yes	—
523	C₄	—	4	4	no	—
524	C₄	—	8	2	no	—
525	C₄	—	8	2	no	—
526	C₄	—	8	2	no	—
527	C₄	—	8	2	no	—
528	C₄	C₅×#385	1	1	yes	characteristic
529	C₄	C₅×#385	1	1	yes	characteristic
530	C₄	C₅×#389	1	1	yes	characteristic
531	C₄	C₅×#389	1	1	yes	characteristic
532	C₄	C₅×#395	1	1	yes	characteristic
533	C₄	C₅×#395	1	1	yes	characteristic
534	C₄	C₅×#398	1	1	yes	characteristic
535	C₄	C₅×#398	1	1	yes	characteristic
536	C₂	C₅×#1444	1	1	yes	characteristic
537	C₂	C₅×#1846	1	1	yes	characteristic
538	C₂	C₅×#1847	1	1	yes	characteristic
539	C₂	C₅×#1854	1	2	yes	—
540	C₂	C₅×#1949	1	2	yes	—
541	C₂	C₅×#2012	1	1	yes	characteristic
542	C₂	C₅×#2015	1	1	yes	characteristic
543	C₂	C₅×#2059	1	2	yes	—
544	C₂	C₅×#2085	1	2	yes	—
545	C₂	C₅×#2092	1	1	yes	characteristic
546	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
27. C₅×#336	C₄	semidirect
28. #11325	C₅	direct (N × H)
185. #336	C₄×C₅	semidirect
499. C₅	#11325	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×#107	2
C₂²×C₅×#106	2
C₂×C₅×#382	2
C₂×C₅×#340	2
C₂×C₅×#336	2
C₅×C₄⋊#95	2
#11325	5

Subgroups — C5×#11325 #11934045

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#11325 #11934045