Subgroups — C₅×#11139 #11933859

Order 1280.

950 conjugacy classes of subgroups.

The subgroup lattice has 578 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#430	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₅×#100	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₅×#100	C₂	1	1	yes	maximal, characteristic
4	C₂²×C₅×#100	C₂	1	1	yes	maximal, characteristic
5	C₅×#1738	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#1738	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₅×#338	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂³×C₅×D₄	C₂²	1	1	yes	characteristic
9	C₂²×C₅×M₁₆	C₂²	1	1	yes	characteristic
10	C₂²×C₅×M₁₆	C₂²	1	1	yes	characteristic
11	C₂²×C₅×M₁₆	C₂²	1	1	yes	characteristic
12	C₂²×C₅×M₁₆	C₂²	1	1	yes	characteristic
13	C₂²×C₅×M₁₆	C₂²	1	1	yes	characteristic
14	C₂²×C₅×M₁₆	C₂²	1	1	yes	characteristic
15	C₅×#430	—	2	2	no	—
16	C₅×#430	—	2	2	no	—
17	C₂×C₅×#108	—	2	2	no	—
18	C₂×C₅×#100	—	2	2	no	—
19	C₂×C₅×#100	—	2	2	no	—
20	C₂×C₅×#100	—	2	2	no	—
21	C₂×C₅×#100	—	2	2	no	—
22	C₂×C₅×#100	—	2	2	no	—
23	C₂×C₅×#100	—	2	2	no	—
24	C₂×C₅×#100	—	2	2	no	—
25	C₂×C₅×#100	—	2	2	no	—
26	C₂×C₅×#100	C₄	1	4	yes	—
27	C₅×#341	—	2	2	no	—
28	C₅×#341	—	2	2	no	—
29	C₅×#338	—	2	2	no	—
30	#11139	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
31	C₂⁵×C₅	Q₈	1	2	yes	—
32	C₂²×C₅×D₄	—	2	1	no	—
33	C₂²×C₅×D₄	—	2	1	no	—
34	C₂²×C₅×D₄	—	2	1	no	—
35	C₂²×C₅×D₄	—	2	1	no	—
36	C₂²×C₅×D₄	—	2	1	no	—
37	C₂²×C₅×D₄	—	2	1	no	—
38	C₂²×C₅×D₄	—	2	1	no	—
39	C₂²×C₅×D₄	—	2	1	no	—
40	C₂²×C₅×D₄	—	2	1	no	—
41	C₂²×C₅×D₄	—	2	1	no	—
42	C₂²×C₅×D₄	—	2	1	no	—
43	C₂²×C₅×D₄	—	2	1	no	—
44	C₂²×C₅×D₄	C₂×C₄	1	2	yes	—
45	C₂²×C₅×D₄	D₄	1	2	yes	—
46	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
47	C₂×C₅×M₁₆	—	2	1	no	—
48	C₂×C₅×M₁₆	—	2	1	no	—
49	C₂×C₅×M₁₆	—	2	1	no	—
50	C₂×C₅×M₁₆	—	2	1	no	—
51	C₂×C₅×M₁₆	—	2	1	no	—
52	C₂×C₅×M₁₆	—	2	1	no	—
53	C₂×C₅×M₁₆	—	2	1	no	—
54	C₂×C₅×M₁₆	—	2	1	no	—
55	C₂×C₅×M₁₆	—	2	1	no	—
56	C₂×C₅×M₁₆	—	2	1	no	—
57	C₂×C₅×M₁₆	—	2	1	no	—
58	C₂×C₅×M₁₆	—	2	1	no	—
59	C₂×C₅×M₁₆	—	2	1	no	—
60	C₂×C₅×M₁₆	—	2	1	no	—
61	C₂×C₅×M₁₆	—	2	1	no	—
62	C₂×C₅×M₁₆	—	2	1	no	—
63	C₂×C₅×M₁₆	—	2	1	no	—
64	C₂×C₅×M₁₆	—	2	1	no	—
65	C₂×C₅×M₁₆	—	2	1	no	—
66	C₂×C₅×M₁₆	—	2	1	no	—
67	C₂×C₅×M₁₆	—	2	1	no	—
68	C₂×C₅×M₁₆	—	2	1	no	—
69	C₂×C₅×M₁₆	—	2	1	no	—
70	C₂×C₅×M₁₆	—	2	1	no	—
71	C₂×C₅×M₁₆	—	2	1	no	—
72	C₂×C₅×M₁₆	—	2	1	no	—
73	C₂×C₅×M₁₆	—	2	1	no	—
74	C₂×C₅×M₁₆	—	2	1	no	—
75	C₂×C₅×M₁₆	C₂×C₄	1	2	yes	—
76	C₂×C₅×M₁₆	C₂×C₄	1	2	yes	—
77	C₂×C₅×M₁₆	D₄	1	2	yes	—
78	C₂×C₅×M₁₆	D₄	1	2	yes	—
79	C₂×C₅×M₁₆	D₄	1	2	yes	—
80	C₂×C₅×M₁₆	D₄	1	2	yes	—
81	C₂×C₅×M₁₆	D₄	1	2	yes	—
82	C₂×C₅×M₁₆	D₄	1	2	yes	—
83	C₂²×C₅×C₈	—	2	1	no	—
84	C₂²×C₅×C₈	—	2	1	no	—
85	C₂²×C₅×C₈	—	2	1	no	—
86	C₂²×C₅×C₈	—	2	1	no	—
87	C₂²×C₅×C₈	—	2	1	no	—
88	C₂²×C₅×C₈	—	2	1	no	—
89	C₅×#108	—	2	8	no	—
90	C₅×#100	—	2	8	no	—
91	C₅×#100	—	2	8	no	—
92	C₅×#100	—	2	8	no	—
93	C₂×#430	C₂×C₅	1	1	yes	characteristic, complemented
94	C₂²×#100	C₂×C₅	1	1	yes	characteristic
95	C₂²×#100	C₂×C₅	1	1	yes	characteristic
96	C₂²×#100	C₂×C₅	1	1	yes	characteristic
97	#1738	C₂×C₅	1	1	yes	characteristic, complemented
98	#1738	C₂×C₅	1	1	yes	characteristic, complemented
99	C₂×#338	C₂×C₅	1	1	yes	characteristic, complemented
100	C₂⁴×C₅	—	2	2	no	—
101	C₂⁴×C₅	—	2	2	no	—
102	C₂⁴×C₅	—	2	2	no	—
103	C₂⁴×C₅	—	2	2	no	—
104	C₂⁴×C₅	—	2	2	no	—
105	C₂⁴×C₅	—	2	2	no	—
106	C₂⁴×C₅	—	8	4	no	—
107	C₂⁴×C₅	C₄⋊C₄	1	4	yes	—
108	C₂⁴×C₅	C₂×Q₈	1	1	yes	characteristic
109	C₂×C₅×D₄	—	2	2	no	—
110	C₂×C₅×D₄	—	2	2	no	—
111	C₂×C₅×D₄	—	2	2	no	—
112	C₂×C₅×D₄	—	2	2	no	—
113	C₂×C₅×D₄	—	2	2	no	—
114	C₂×C₅×D₄	—	2	2	no	—
115	C₂×C₅×D₄	—	2	2	no	—
116	C₂×C₅×D₄	—	2	2	no	—
117	C₂×C₅×D₄	—	2	2	no	—
118	C₂×C₅×D₄	—	2	2	no	—
119	C₂×C₅×D₄	—	2	2	no	—
120	C₂×C₅×D₄	—	2	2	no	—
121	C₂×C₅×D₄	—	4	1	no	—
122	C₂×C₅×D₄	—	4	1	no	—
123	C₂×C₅×D₄	—	4	1	no	—
124	C₂×C₅×D₄	—	4	1	no	—
125	C₂×C₅×D₄	—	4	1	no	—
126	C₂×C₅×D₄	—	4	1	no	—
127	C₂×C₅×D₄	—	4	1	no	—
128	C₂×C₅×D₄	—	4	1	no	—
129	C₂×C₅×D₄	—	4	1	no	—
130	C₂×C₅×D₄	—	4	1	no	—
131	C₂×C₅×D₄	—	4	1	no	—
132	C₂×C₅×D₄	—	4	1	no	—
133	C₂×C₅×D₄	—	4	1	no	—
134	C₂×C₅×D₄	—	4	1	no	—
135	C₂×C₅×D₄	—	4	1	no	—
136	C₂×C₅×D₄	—	4	1	no	—
137	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
138	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
139	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
140	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
141	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
142	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
143	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
144	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
145	C₂²×C₄×C₅	#41	1	1	yes	characteristic
146	C₂²×C₄×C₅	#41	1	1	yes	characteristic
147	C₂²×C₄×C₅	#41	1	1	yes	characteristic
148	C₂²×C₄×C₅	#41	1	1	yes	characteristic
149	C₂²×C₄×C₅	#41	1	1	yes	characteristic
150	C₂²×C₄×C₅	#41	1	1	yes	characteristic
151	C₅×M₁₆	—	2	2	no	—
152	C₅×M₁₆	—	2	2	no	—
153	C₅×M₁₆	—	2	2	no	—
154	C₅×M₁₆	—	2	2	no	—
155	C₅×M₁₆	—	2	2	no	—
156	C₅×M₁₆	—	2	2	no	—
157	C₅×M₁₆	—	2	2	no	—
158	C₅×M₁₆	—	2	2	no	—
159	C₅×M₁₆	—	2	2	no	—
160	C₅×M₁₆	—	2	2	no	—
161	C₅×M₁₆	—	2	2	no	—
162	C₅×M₁₆	—	2	2	no	—
163	C₅×M₁₆	—	2	2	no	—
164	C₅×M₁₆	—	4	1	no	—
165	C₅×M₁₆	—	4	1	no	—
166	C₅×M₁₆	—	4	1	no	—
167	C₅×M₁₆	—	4	1	no	—
168	C₅×M₁₆	—	4	1	no	—
169	C₅×M₁₆	—	4	1	no	—
170	C₅×M₁₆	—	4	1	no	—
171	C₅×M₁₆	—	4	1	no	—
172	C₅×M₁₆	—	4	1	no	—
173	C₅×M₁₆	—	4	1	no	—
174	C₅×M₁₆	C₂²⋊C₄	1	4	yes	—
175	C₂×C₅×C₈	—	2	2	no	—
176	C₂×C₅×C₈	—	2	2	no	—
177	C₂×C₅×C₈	—	2	2	no	—
178	C₂×C₅×C₈	—	2	2	no	—
179	C₂×C₅×C₈	—	2	2	no	—
180	C₂×C₅×C₈	—	2	2	no	—
181	C₂×C₅×C₈	—	2	2	no	—
182	C₂×C₅×C₈	—	2	2	no	—
183	C₂×C₅×C₈	—	4	1	no	—
184	C₂×C₅×C₈	—	4	1	no	—
185	C₂×C₅×C₈	—	4	1	no	—
186	C₂×C₅×C₈	—	4	1	no	—
187	C₂×C₅×C₈	—	4	1	no	—
188	C₂×C₅×C₈	—	4	1	no	—
189	C₂×C₅×C₈	—	4	1	no	—
190	C₂×C₅×C₈	—	4	1	no	—
191	C₂×C₅×C₈	—	4	1	no	—
192	C₂×C₅×C₈	—	4	1	no	—
193	C₂³×D₄	C₂²×C₅	1	1	yes	characteristic
194	C₂²×M₁₆	C₂²×C₅	1	1	yes	characteristic
195	C₂²×M₁₆	C₂²×C₅	1	1	yes	characteristic
196	C₂²×M₁₆	C₂²×C₅	1	1	yes	characteristic
197	C₂²×M₁₆	C₂²×C₅	1	1	yes	characteristic
198	C₂²×M₁₆	C₂²×C₅	1	1	yes	characteristic
199	C₂²×M₁₆	C₂²×C₅	1	1	yes	characteristic
200	#430	—	2	2	no	—
201	#430	—	2	2	no	—
202	C₂×#108	—	2	2	no	—
203	C₂×#100	—	2	2	no	—
204	C₂×#100	—	2	2	no	—
205	C₂×#100	—	2	2	no	—
206	C₂×#100	—	2	2	no	—
207	C₂×#100	—	2	2	no	—
208	C₂×#100	—	2	2	no	—
209	C₂×#100	—	2	2	no	—
210	C₂×#100	—	2	2	no	—
211	C₂×#100	C₄×C₅	1	4	yes	—
212	#341	—	2	2	no	—
213	#341	—	2	2	no	—
214	#338	—	2	2	no	—
215	C₂³×C₅	—	2	4	no	—
216	C₂³×C₅	—	2	4	no	—
217	C₂³×C₅	—	2	4	no	—
218	C₂³×C₅	—	4	2	no	—
219	C₂³×C₅	—	4	2	no	—
220	C₂³×C₅	—	4	2	no	—
221	C₂³×C₅	—	4	2	no	—
222	C₂³×C₅	—	4	2	no	—
223	C₂³×C₅	—	8	4	no	—
224	C₂³×C₅	—	8	4	no	—
225	C₂³×C₅	—	8	4	no	—
226	C₂³×C₅	—	8	4	no	—
227	C₂³×C₅	—	8	4	no	—
228	C₂³×C₅	—	8	4	no	—
229	C₂³×C₅	—	8	4	no	—
230	C₂³×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
231	C₂³×C₅	C₂²⋊Q₈	1	1	yes	characteristic
232	C₂³×C₅	C₂²⋊Q₈	1	1	yes	characteristic
233	C₂³×C₅	C₂²⋊Q₈	1	1	yes	characteristic
234	C₂³×C₅	C₂²⋊Q₈	1	1	yes	characteristic
235	C₂³×C₅	C₂²⋊Q₈	1	1	yes	characteristic
236	C₂³×C₅	C₂²⋊Q₈	1	1	yes	characteristic
237	C₅×D₄	—	4	2	no	—
238	C₅×D₄	—	4	2	no	—
239	C₅×D₄	—	4	2	no	—
240	C₅×D₄	—	4	2	no	—
241	C₅×D₄	—	4	2	no	—
242	C₅×D₄	—	4	2	no	—
243	C₅×D₄	—	4	2	no	—
244	C₅×D₄	—	4	2	no	—
245	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
246	C₂×C₄×C₅	#117	1	1	yes	characteristic
247	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
248	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
249	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
250	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
251	C₂×C₄×C₅	#120	1	1	yes	characteristic
252	C₂×C₄×C₅	#120	1	1	yes	characteristic
253	C₂×C₄×C₅	#120	1	1	yes	characteristic
254	C₂×C₄×C₅	#121	1	1	yes	characteristic
255	C₂×C₄×C₅	#121	1	1	yes	characteristic
256	C₂×C₄×C₅	#121	1	1	yes	characteristic
257	C₂×C₄×C₅	#121	1	1	yes	characteristic
258	C₂×C₄×C₅	#121	1	1	yes	characteristic
259	C₂×C₄×C₅	#121	1	1	yes	characteristic
260	C₂×C₄×C₅	#121	1	1	yes	characteristic
261	C₂×C₄×C₅	#121	1	1	yes	characteristic
262	C₂×C₄×C₅	#123	1	1	yes	characteristic
263	C₂×C₄×C₅	#123	1	1	yes	characteristic
264	C₂×C₄×C₅	#123	1	1	yes	characteristic
265	C₂×C₄×C₅	#123	1	1	yes	characteristic
266	C₂×C₄×C₅	#123	1	1	yes	characteristic
267	C₂×C₄×C₅	#124	1	1	yes	characteristic
268	C₂×C₄×C₅	#124	1	1	yes	characteristic
269	C₂×C₄×C₅	#124	1	1	yes	characteristic
270	C₂×C₄×C₅	#126	1	1	yes	characteristic
271	C₂×C₄×C₅	#126	1	1	yes	characteristic
272	C₂×C₄×C₅	#127	1	1	yes	characteristic
273	C₅×C₈	—	2	4	no	—
274	C₅×C₈	—	4	2	no	—
275	C₅×C₈	—	4	2	no	—
276	C₅×C₈	—	4	2	no	—
277	C₅×C₈	—	4	2	no	—
278	C₅×C₈	—	4	2	no	—
279	C₂⁵	C₅×Q₈	1	2	yes	—
280	C₂²×D₄	—	2	1	no	—
281	C₂²×D₄	—	2	1	no	—
282	C₂²×D₄	—	2	1	no	—
283	C₂²×D₄	—	2	1	no	—
284	C₂²×D₄	—	2	1	no	—
285	C₂²×D₄	—	2	1	no	—
286	C₂²×D₄	—	2	1	no	—
287	C₂²×D₄	—	2	1	no	—
288	C₂²×D₄	—	2	1	no	—
289	C₂²×D₄	—	2	1	no	—
290	C₂²×D₄	—	2	1	no	—
291	C₂²×D₄	—	2	1	no	—
292	C₂²×D₄	C₂×C₄×C₅	1	2	yes	—
293	C₂²×D₄	C₅×D₄	1	2	yes	—
294	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
295	C₂×M₁₆	—	2	1	no	—
296	C₂×M₁₆	—	2	1	no	—
297	C₂×M₁₆	—	2	1	no	—
298	C₂×M₁₆	—	2	1	no	—
299	C₂×M₁₆	—	2	1	no	—
300	C₂×M₁₆	—	2	1	no	—
301	C₂×M₁₆	—	2	1	no	—
302	C₂×M₁₆	—	2	1	no	—
303	C₂×M₁₆	—	2	1	no	—
304	C₂×M₁₆	—	2	1	no	—
305	C₂×M₁₆	—	2	1	no	—
306	C₂×M₁₆	—	2	1	no	—
307	C₂×M₁₆	—	2	1	no	—
308	C₂×M₁₆	—	2	1	no	—
309	C₂×M₁₆	—	2	1	no	—
310	C₂×M₁₆	—	2	1	no	—
311	C₂×M₁₆	—	2	1	no	—
312	C₂×M₁₆	—	2	1	no	—
313	C₂×M₁₆	—	2	1	no	—
314	C₂×M₁₆	—	2	1	no	—
315	C₂×M₁₆	—	2	1	no	—
316	C₂×M₁₆	—	2	1	no	—
317	C₂×M₁₆	—	2	1	no	—
318	C₂×M₁₆	—	2	1	no	—
319	C₂×M₁₆	—	2	1	no	—
320	C₂×M₁₆	—	2	1	no	—
321	C₂×M₁₆	—	2	1	no	—
322	C₂×M₁₆	—	2	1	no	—
323	C₂×M₁₆	C₂×C₄×C₅	1	2	yes	—
324	C₂×M₁₆	C₂×C₄×C₅	1	2	yes	—
325	C₂×M₁₆	C₅×D₄	1	2	yes	—
326	C₂×M₁₆	C₅×D₄	1	2	yes	—
327	C₂×M₁₆	C₅×D₄	1	2	yes	—
328	C₂×M₁₆	C₅×D₄	1	2	yes	—
329	C₂×M₁₆	C₅×D₄	1	2	yes	—
330	C₂×M₁₆	C₅×D₄	1	2	yes	—
331	C₂²×C₈	—	2	1	no	—
332	C₂²×C₈	—	2	1	no	—
333	C₂²×C₈	—	2	1	no	—
334	C₂²×C₈	—	2	1	no	—
335	C₂²×C₈	—	2	1	no	—
336	C₂²×C₈	—	2	1	no	—
337	#108	—	2	8	no	—
338	#100	—	2	8	no	—
339	#100	—	2	8	no	—
340	#100	—	2	8	no	—
341	C₂²×C₅	—	2	2	no	—
342	C₂²×C₅	—	2	2	no	—
343	C₂²×C₅	—	2	2	no	—
344	C₂²×C₅	—	4	1	no	—
345	C₂²×C₅	—	4	1	no	—
346	C₂²×C₅	—	4	1	no	—
347	C₂²×C₅	—	4	1	no	—
348	C₂²×C₅	—	4	4	no	—
349	C₂²×C₅	—	8	4	no	—
350	C₂²×C₅	—	8	4	no	—
351	C₂²×C₅	—	8	4	no	—
352	C₂²×C₅	—	8	4	no	—
353	C₂²×C₅	—	8	4	no	—
354	C₂²×C₅	—	8	4	no	—
355	C₂²×C₅	—	8	4	no	—
356	C₂²×C₅	#380	1	1	yes	characteristic
357	C₂²×C₅	#385	1	1	yes	characteristic
358	C₂²×C₅	#385	1	1	yes	characteristic
359	C₂²×C₅	#393	1	1	yes	characteristic
360	C₂²×C₅	#396	1	1	yes	characteristic
361	C₂²×C₅	#396	1	1	yes	characteristic
362	C₂²×C₅	#399	1	1	yes	characteristic
363	C₄×C₅	#386	1	1	yes	characteristic
364	C₄×C₅	#388	1	1	yes	characteristic
365	C₄×C₅	#388	1	1	yes	characteristic
366	C₄×C₅	#390	1	1	yes	characteristic
367	C₄×C₅	#392	1	1	yes	characteristic
368	C₄×C₅	#394	1	1	yes	characteristic
369	C₄×C₅	#394	1	1	yes	characteristic
370	C₄×C₅	#397	1	1	yes	characteristic
371	C₂⁴	—	2	2	no	—
372	C₂⁴	—	2	2	no	—
373	C₂⁴	—	2	2	no	—
374	C₂⁴	—	2	2	no	—
375	C₂⁴	—	2	2	no	—
376	C₂⁴	—	2	2	no	—
377	C₂⁴	—	8	4	no	—
378	C₂⁴	C₅×C₄⋊C₄	1	4	yes	—
379	C₂⁴	C₂×C₅×Q₈	1	1	yes	characteristic
380	C₂×D₄	—	2	2	no	—
381	C₂×D₄	—	2	2	no	—
382	C₂×D₄	—	2	2	no	—
383	C₂×D₄	—	2	2	no	—
384	C₂×D₄	—	2	2	no	—
385	C₂×D₄	—	2	2	no	—
386	C₂×D₄	—	2	2	no	—
387	C₂×D₄	—	2	2	no	—
388	C₂×D₄	—	2	2	no	—
389	C₂×D₄	—	2	2	no	—
390	C₂×D₄	—	2	2	no	—
391	C₂×D₄	—	2	2	no	—
392	C₂×D₄	—	4	1	no	—
393	C₂×D₄	—	4	1	no	—
394	C₂×D₄	—	4	1	no	—
395	C₂×D₄	—	4	1	no	—
396	C₂×D₄	—	4	1	no	—
397	C₂×D₄	—	4	1	no	—
398	C₂×D₄	—	4	1	no	—
399	C₂×D₄	—	4	1	no	—
400	C₂×D₄	—	4	1	no	—
401	C₂×D₄	—	4	1	no	—
402	C₂×D₄	—	4	1	no	—
403	C₂×D₄	—	4	1	no	—
404	C₂×D₄	—	4	1	no	—
405	C₂×D₄	—	4	1	no	—
406	C₂×D₄	—	4	1	no	—
407	C₂×D₄	—	4	1	no	—
408	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
409	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
410	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
411	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
412	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
413	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
414	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
415	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
416	C₂²×C₄	C₅×#41	1	1	yes	characteristic
417	C₂²×C₄	C₅×#41	1	1	yes	characteristic
418	C₂²×C₄	C₅×#41	1	1	yes	characteristic
419	C₂²×C₄	C₅×#41	1	1	yes	characteristic
420	C₂²×C₄	C₅×#41	1	1	yes	characteristic
421	C₂²×C₄	C₅×#41	1	1	yes	characteristic
422	M₁₆	—	2	2	no	—
423	M₁₆	—	2	2	no	—
424	M₁₆	—	2	2	no	—
425	M₁₆	—	2	2	no	—
426	M₁₆	—	2	2	no	—
427	M₁₆	—	2	2	no	—
428	M₁₆	—	2	2	no	—
429	M₁₆	—	2	2	no	—
430	M₁₆	—	2	2	no	—
431	M₁₆	—	2	2	no	—
432	M₁₆	—	2	2	no	—
433	M₁₆	—	2	2	no	—
434	M₁₆	—	2	2	no	—
435	M₁₆	—	4	1	no	—
436	M₁₆	—	4	1	no	—
437	M₁₆	—	4	1	no	—
438	M₁₆	—	4	1	no	—
439	M₁₆	—	4	1	no	—
440	M₁₆	—	4	1	no	—
441	M₁₆	—	4	1	no	—
442	M₁₆	—	4	1	no	—
443	M₁₆	—	4	1	no	—
444	M₁₆	—	4	1	no	—
445	M₁₆	C₅×C₂²⋊C₄	1	4	yes	—
446	C₂×C₈	—	2	2	no	—
447	C₂×C₈	—	2	2	no	—
448	C₂×C₈	—	2	2	no	—
449	C₂×C₈	—	2	2	no	—
450	C₂×C₈	—	2	2	no	—
451	C₂×C₈	—	2	2	no	—
452	C₂×C₈	—	2	2	no	—
453	C₂×C₈	—	2	2	no	—
454	C₂×C₈	—	4	1	no	—
455	C₂×C₈	—	4	1	no	—
456	C₂×C₈	—	4	1	no	—
457	C₂×C₈	—	4	1	no	—
458	C₂×C₈	—	4	1	no	—
459	C₂×C₈	—	4	1	no	—
460	C₂×C₈	—	4	1	no	—
461	C₂×C₈	—	4	1	no	—
462	C₂×C₈	—	4	1	no	—
463	C₂×C₈	—	4	1	no	—
464	C₂×C₅	—	2	1	no	—
465	C₂×C₅	—	2	1	no	—
466	C₂×C₅	—	2	1	no	—
467	C₂×C₅	—	2	1	no	—
468	C₂×C₅	—	2	1	no	—
469	C₂×C₅	—	2	1	no	—
470	C₂×C₅	—	8	4	no	—
471	C₂×C₅	#1439	1	1	yes	characteristic
472	C₂×C₅	#2069	1	2	yes	—
473	C₂³	—	2	4	no	—
474	C₂³	—	2	4	no	—
475	C₂³	—	2	4	no	—
476	C₂³	—	4	2	no	—
477	C₂³	—	4	2	no	—
478	C₂³	—	4	2	no	—
479	C₂³	—	4	2	no	—
480	C₂³	—	4	2	no	—
481	C₂³	—	8	4	no	—
482	C₂³	—	8	4	no	—
483	C₂³	—	8	4	no	—
484	C₂³	—	8	4	no	—
485	C₂³	—	8	4	no	—
486	C₂³	—	8	4	no	—
487	C₂³	—	8	4	no	—
488	C₂³	C₂×C₅×C₄⋊C₄	1	1	yes	characteristic
489	C₂³	C₅×C₂²⋊Q₈	1	1	yes	characteristic
490	C₂³	C₅×C₂²⋊Q₈	1	1	yes	characteristic
491	C₂³	C₅×C₂²⋊Q₈	1	1	yes	characteristic
492	C₂³	C₅×C₂²⋊Q₈	1	1	yes	characteristic
493	C₂³	C₅×C₂²⋊Q₈	1	1	yes	characteristic
494	C₂³	C₅×C₂²⋊Q₈	1	1	yes	characteristic
495	D₄	—	4	2	no	—
496	D₄	—	4	2	no	—
497	D₄	—	4	2	no	—
498	D₄	—	4	2	no	—
499	D₄	—	4	2	no	—
500	D₄	—	4	2	no	—
501	D₄	—	4	2	no	—
502	D₄	—	4	2	no	—
503	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
504	C₂×C₄	C₅×#117	1	1	yes	characteristic
505	C₂×C₄	C₄×C₅×D₄	1	1	yes	characteristic
506	C₂×C₄	C₄×C₅×D₄	1	1	yes	characteristic
507	C₂×C₄	C₄×C₅×D₄	1	1	yes	characteristic
508	C₂×C₄	C₄×C₅×D₄	1	1	yes	characteristic
509	C₂×C₄	C₅×#120	1	1	yes	characteristic
510	C₂×C₄	C₅×#120	1	1	yes	characteristic
511	C₂×C₄	C₅×#120	1	1	yes	characteristic
512	C₂×C₄	C₅×#121	1	1	yes	characteristic
513	C₂×C₄	C₅×#121	1	1	yes	characteristic
514	C₂×C₄	C₅×#121	1	1	yes	characteristic
515	C₂×C₄	C₅×#121	1	1	yes	characteristic
516	C₂×C₄	C₅×#121	1	1	yes	characteristic
517	C₂×C₄	C₅×#121	1	1	yes	characteristic
518	C₂×C₄	C₅×#121	1	1	yes	characteristic
519	C₂×C₄	C₅×#121	1	1	yes	characteristic
520	C₂×C₄	C₅×#123	1	1	yes	characteristic
521	C₂×C₄	C₅×#123	1	1	yes	characteristic
522	C₂×C₄	C₅×#123	1	1	yes	characteristic
523	C₂×C₄	C₅×#123	1	1	yes	characteristic
524	C₂×C₄	C₅×#123	1	1	yes	characteristic
525	C₂×C₄	C₅×#124	1	1	yes	characteristic
526	C₂×C₄	C₅×#124	1	1	yes	characteristic
527	C₂×C₄	C₅×#124	1	1	yes	characteristic
528	C₂×C₄	C₅×#126	1	1	yes	characteristic
529	C₂×C₄	C₅×#126	1	1	yes	characteristic
530	C₂×C₄	C₅×#127	1	1	yes	characteristic
531	C₈	—	2	4	no	—
532	C₈	—	4	2	no	—
533	C₈	—	4	2	no	—
534	C₈	—	4	2	no	—
535	C₈	—	4	2	no	—
536	C₈	—	4	2	no	—
537	C₅	#11139	1	1	yes	characteristic, direct product factor, Sylow
538	C₂²	—	2	2	no	—
539	C₂²	—	2	2	no	—
540	C₂²	—	2	2	no	—
541	C₂²	—	4	1	no	—
542	C₂²	—	4	1	no	—
543	C₂²	—	4	1	no	—
544	C₂²	—	4	1	no	—
545	C₂²	—	4	4	no	—
546	C₂²	—	8	4	no	—
547	C₂²	—	8	4	no	—
548	C₂²	—	8	4	no	—
549	C₂²	—	8	4	no	—
550	C₂²	—	8	4	no	—
551	C₂²	—	8	4	no	—
552	C₂²	—	8	4	no	—
553	C₂²	C₅×#380	1	1	yes	characteristic
554	C₂²	C₅×#385	1	1	yes	characteristic
555	C₂²	C₅×#385	1	1	yes	characteristic
556	C₂²	C₅×#393	1	1	yes	characteristic
557	C₂²	C₅×#396	1	1	yes	characteristic
558	C₂²	C₅×#396	1	1	yes	characteristic
559	C₂²	C₅×#399	1	1	yes	characteristic
560	C₄	C₅×#386	1	1	yes	characteristic
561	C₄	C₅×#388	1	1	yes	characteristic
562	C₄	C₅×#388	1	1	yes	characteristic
563	C₄	C₅×#390	1	1	yes	characteristic
564	C₄	C₅×#392	1	1	yes	characteristic
565	C₄	C₅×#394	1	1	yes	characteristic
566	C₄	C₅×#394	1	1	yes	characteristic
567	C₄	C₅×#397	1	1	yes	characteristic
568	C₂	—	2	1	no	—
569	C₂	—	2	1	no	—
570	C₂	—	2	1	no	—
571	C₂	—	2	1	no	—
572	C₂	—	2	1	no	—
573	C₂	—	2	1	no	—
574	C₂	—	8	4	no	—
575	C₂	C₅×#1439	1	1	yes	characteristic
576	C₂	C₅×#2069	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₅	#396
commutator	C₂²×C₄	C₂²×C₄×C₅
Frattini, cosocle	C₂³×C₄	C₂³×C₅
prime radical	C₂³×C₅×D₄	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₅ ◁ C₂³×C₄×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₅×#430	C₂	semidirect
5. C₅×#1738	C₂	semidirect
6. C₅×#1738	C₂	semidirect
7. C₂×C₅×#338	C₂	semidirect
30. #11139	C₅	direct (N × H)
93. C₂×#430	C₂×C₅	semidirect
97. #1738	C₂×C₅	semidirect
98. #1738	C₂×C₅	semidirect
99. C₂×#338	C₂×C₅	semidirect
537. C₅	#11139	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×#430	2
C₂²×C₅×#100	2
C₅×#1738	2
C₂×C₅×#338	2
#11139	5

Subgroups — C5×#11139 #11933859

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#11139 #11933859