Subgroups — C₂×#10601523 #12128016

Order 1280.

1078 conjugacy classes of subgroups.

The subgroup lattice has 592 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×#3955	C₂	1	1	yes	maximal, characteristic
3	C₂²×#3955	C₂	1	1	yes	maximal, characteristic
4	C₂²×#3955	C₂	1	1	yes	maximal, characteristic
5	C₂×#65414	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#65413	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#64780	C₂	1	1	yes	maximal, characteristic, complemented
8	#10601523	C₂	1	8	yes	maximal, direct product factor
9	C₂³×D₂₀	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×#681	C₂²	1	1	yes	characteristic
14	C₂²×#681	C₂²	1	1	yes	characteristic
15	C₂²×#681	C₂²	1	1	yes	characteristic
16	C₅×#430	—	2	2	no	—
17	C₅×#430	C₂²	1	4	yes	complemented
18	C₂×C₅×#108	—	2	2	no	—
19	C₂×#3955	—	2	2	no	—
20	C₂×#3955	—	2	2	no	—
21	C₂×#3955	—	2	2	no	—
22	C₂×#3955	—	2	2	no	—
23	C₂×#3955	—	2	2	no	—
24	C₂×#3955	—	2	2	no	—
25	C₂×#3955	C₂²	1	4	yes	—
26	C₂×#3955	C₂²	1	4	yes	—
27	C₂×#3955	C₂²	1	4	yes	—
28	#65414	—	2	2	no	—
29	#65414	C₂²	1	4	yes	complemented
30	#65413	—	2	2	no	—
31	#65413	C₂²	1	4	yes	complemented
32	C₂×#3954	—	2	2	no	—
33	C₂×#3951	—	2	2	no	—
34	#64780	C₂²	1	4	yes	complemented
35	C₂×#2069	—	5	1	no	maximal, Sylow
36	C₂⁴×D₅	Q₈	1	2	yes	—
37	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
38	C₂²×D₂₀	—	2	1	no	—
39	C₂²×D₂₀	—	2	1	no	—
40	C₂²×D₂₀	—	2	1	no	—
41	C₂²×D₂₀	—	2	1	no	—
42	C₂²×D₂₀	—	2	1	no	—
43	C₂²×D₂₀	—	2	1	no	—
44	C₂²×D₂₀	—	2	1	no	—
45	C₂²×D₂₀	—	2	1	no	—
46	C₂²×D₂₀	—	2	1	no	—
47	C₂²×D₂₀	—	2	1	no	—
48	C₂²×D₂₀	—	2	1	no	—
49	C₂²×D₂₀	—	2	1	no	—
50	C₂²×D₂₀	Q₈	1	2	yes	—
51	C₂²×D₂₀	C₂³	1	2	yes	—
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	D₄	1	2	yes	—
64	C₂×C₅×M₁₆	D₄	1	2	yes	—
65	C₂×C₅×M₁₆	D₄	1	2	yes	—
66	C₂×C₅×M₁₆	D₄	1	2	yes	—
67	C₂×C₅×M₁₆	C₂³	1	2	yes	—
68	C₂×C₅×M₁₆	C₂³	1	2	yes	—
69	C₂×C₅×M₁₆	C₂³	1	2	yes	—
70	C₂²×C₅×C₈	—	2	1	no	—
71	C₂²×C₅×C₈	—	2	1	no	—
72	C₂²×C₅×C₈	—	2	1	no	—
73	C₂×#681	—	2	1	no	—
74	C₂×#681	—	2	1	no	—
75	C₂×#681	—	2	1	no	—
76	C₂×#681	—	2	1	no	—
77	C₂×#681	—	2	1	no	—
78	C₂×#681	—	2	1	no	—
79	C₂×#681	—	2	1	no	—
80	C₂×#681	—	2	1	no	—
81	C₂×#681	—	2	1	no	—
82	C₂×#681	—	2	1	no	—
83	C₂×#681	—	2	1	no	—
84	C₂×#681	—	2	1	no	—
85	C₂×#681	—	2	1	no	—
86	C₂×#681	D₄	1	2	yes	—
87	C₂×#681	D₄	1	2	yes	—
88	C₂×#681	C₂³	1	2	yes	—
89	C₂×#681	C₂³	1	2	yes	—
90	C₂×#681	C₂³	1	2	yes	—
91	C₂²×#168	—	2	1	no	—
92	C₂²×#168	—	2	1	no	—
93	C₂²×#168	—	2	1	no	—
94	C₅×#108	—	2	8	no	—
95	#3955	—	2	8	no	—
96	#3955	—	2	8	no	—
97	#3955	—	2	8	no	—
98	#3954	—	2	8	no	—
99	#3951	—	2	8	no	—
100	C₂×#430	—	5	1	no	—
101	C₂×#430	—	5	1	no	—
102	C₂×#430	D₅	1	1	yes	characteristic, complemented
103	C₂²×#100	—	5	1	no	—
104	C₂²×#100	—	5	1	no	—
105	C₂²×#100	—	5	1	no	—
106	#2069	—	5	8	no	—
107	C₂×#338	—	5	1	no	—
108	C₂⁴×C₅	C₂×Q₈	1	1	yes	characteristic
109	C₂³×D₅	—	2	2	no	—
110	C₂³×D₅	—	2	2	no	—
111	C₂³×D₅	—	2	2	no	—
112	C₂³×D₅	—	2	2	no	—
113	C₂³×D₅	—	2	2	no	—
114	C₂³×D₅	—	2	2	no	—
115	C₂³×D₅	—	8	4	no	—
116	C₂³×D₅	C₂×Q₈	1	4	yes	—
117	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
118	C₂²×C₄×C₅	C₂×D₄	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×Q₈	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	C₂²×C₄×C₅	#41	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	C₂⁴	1	1	yes	characteristic
131	C₂×D₂₀	—	2	2	no	—
132	C₂×D₂₀	—	2	2	no	—
133	C₂×D₂₀	—	2	2	no	—
134	C₂×D₂₀	—	2	2	no	—
135	C₂×D₂₀	—	2	2	no	—
136	C₂×D₂₀	—	2	2	no	—
137	C₂×D₂₀	—	2	2	no	—
138	C₂×D₂₀	—	2	2	no	—
139	C₂×D₂₀	—	2	2	no	—
140	C₂×D₂₀	—	2	2	no	—
141	C₂×D₂₀	—	2	2	no	—
142	C₂×D₂₀	—	2	2	no	—
143	C₂×D₂₀	—	4	1	no	—
144	C₂×D₂₀	—	4	1	no	—
145	C₂×D₂₀	—	4	1	no	—
146	C₂×D₂₀	—	4	1	no	—
147	C₂×D₂₀	—	4	1	no	—
148	C₂×D₂₀	—	4	1	no	—
149	C₂×D₂₀	—	4	1	no	—
150	C₂×D₂₀	—	4	1	no	—
151	C₂×D₂₀	—	4	1	no	—
152	C₂×D₂₀	—	4	1	no	—
153	C₂×D₂₀	—	4	1	no	—
154	C₂×D₂₀	—	4	1	no	—
155	C₂×D₂₀	—	4	1	no	—
156	C₂×D₂₀	—	4	1	no	—
157	C₂×D₂₀	—	4	1	no	—
158	C₂×D₂₀	—	4	1	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	—	2	2	no	—
165	C₅×M₁₆	—	2	2	no	—
166	C₅×M₁₆	—	2	2	no	—
167	C₅×M₁₆	—	4	1	no	—
168	C₅×M₁₆	—	4	1	no	—
169	C₅×M₁₆	C₂×D₄	1	4	yes	—
170	C₅×M₁₆	C₂×D₄	1	4	yes	—
171	C₂×C₅×C₈	—	2	2	no	—
172	C₂×C₅×C₈	—	2	2	no	—
173	C₂×C₅×C₈	—	2	2	no	—
174	C₂×C₅×C₈	—	2	2	no	—
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	—	4	1	no	—
179	C₂×C₅×C₈	—	4	1	no	—
180	#681	—	2	2	no	—
181	#681	—	2	2	no	—
182	#681	—	2	2	no	—
183	#681	—	2	2	no	—
184	#681	—	2	2	no	—
185	#681	—	2	2	no	—
186	#681	—	2	2	no	—
187	#681	—	4	1	no	—
188	#681	—	4	1	no	—
189	#681	—	4	1	no	—
190	#681	—	4	1	no	—
191	#681	C₂×D₄	1	4	yes	—
192	C₂×#168	—	2	2	no	—
193	C₂×#168	—	2	2	no	—
194	C₂×#168	—	2	2	no	—
195	C₂×#168	—	2	2	no	—
196	C₂×#168	—	2	2	no	—
197	C₂×#168	—	4	1	no	—
198	C₂×#168	—	4	1	no	—
199	C₂×#168	—	4	1	no	—
200	C₂×#168	—	4	1	no	—
201	C₂³×D₄	—	5	1	no	—
202	C₂²×M₁₆	—	5	1	no	—
203	C₂²×M₁₆	—	5	1	no	—
204	C₂²×M₁₆	—	5	1	no	—
205	C₂²×M₁₆	C₂×D₅	1	1	yes	characteristic
206	C₂²×M₁₆	C₂×D₅	1	1	yes	characteristic
207	C₂²×M₁₆	C₂×D₅	1	1	yes	characteristic
208	#430	—	2	2	no	—
209	#430	—	5	4	no	—
210	#430	—	5	4	no	—
211	#430	—	10	2	no	—
212	#430	—	10	2	no	—
213	#430	C₂×D₅	1	4	yes	complemented
214	C₂×#108	—	2	2	no	—
215	C₂×#108	—	10	2	no	—
216	C₂×#108	—	10	2	no	—
217	C₂×#100	—	5	4	no	—
218	C₂×#100	—	5	4	no	—
219	C₂×#100	—	5	4	no	—
220	C₂×#100	—	10	2	no	—
221	C₂×#100	—	10	2	no	—
222	C₂×#100	—	10	2	no	—
223	C₂×#100	—	10	2	no	—
224	C₂×#100	—	10	2	no	—
225	C₂×#100	—	10	2	no	—
226	#338	—	5	4	no	—
227	C₂³×C₅	—	4	2	no	—
228	C₂³×C₅	C₂²⋊Q₈	1	1	yes	characteristic
229	C₂³×C₅	C₂²⋊Q₈	1	1	yes	characteristic
230	C₂³×C₅	C₂²⋊Q₈	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	C₂²×D₅	—	2	4	no	—
236	C₂²×D₅	—	2	4	no	—
237	C₂²×D₅	—	2	4	no	—
238	C₂²×D₅	—	4	2	no	—
239	C₂²×D₅	—	4	2	no	—
240	C₂²×D₅	—	4	2	no	—
241	C₂²×D₅	—	4	2	no	—
242	C₂²×D₅	—	8	4	no	—
243	C₂²×D₅	—	8	4	no	—
244	C₂²×D₅	—	8	4	no	—
245	C₂²×D₅	—	8	4	no	—
246	C₂²×D₅	—	8	4	no	—
247	C₂²×D₅	—	8	4	no	—
248	C₂²×D₅	—	8	4	no	—
249	C₂×C₄×C₅	#121	1	1	yes	characteristic
250	C₂×C₄×C₅	#121	1	1	yes	characteristic
251	C₂×C₄×C₅	#121	1	1	yes	characteristic
252	C₂×C₄×C₅	#121	1	1	yes	characteristic
253	C₂×C₄×C₅	#121	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	C₂²⋊Q₈	1	1	yes	characteristic
262	C₂×C₄×C₅	C₂²⋊Q₈	1	1	yes	characteristic
263	C₂×C₄×C₅	C₂²⋊Q₈	1	1	yes	characteristic
264	C₂×C₄×C₅	C₂²⋊Q₈	1	1	yes	characteristic
265	C₂×C₄×C₅	C₂²⋊Q₈	1	1	yes	characteristic
266	C₂×C₄×C₅	C₂²⋊Q₈	1	1	yes	characteristic
267	C₂×C₄×C₅	#126	1	1	yes	characteristic
268	C₂×C₄×C₅	#126	1	1	yes	characteristic
269	C₂×C₄×C₅	#126	1	1	yes	characteristic
270	C₂×C₄×C₅	#126	1	1	yes	characteristic
271	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
272	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
273	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
274	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
275	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
276	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
277	D₂₀	—	4	2	no	—
278	D₂₀	—	4	2	no	—
279	D₂₀	—	4	2	no	—
280	D₂₀	—	4	2	no	—
281	D₂₀	—	4	2	no	—
282	D₂₀	—	4	2	no	—
283	D₂₀	—	4	2	no	—
284	D₂₀	—	4	2	no	—
285	C₅×C₈	—	2	4	no	—
286	C₅×C₈	—	2	4	no	—
287	C₅×C₈	—	4	2	no	—
288	#168	—	2	4	no	—
289	#168	—	4	2	no	—
290	#168	—	4	2	no	—
291	C₂⁵	—	5	2	no	—
292	C₂²×D₄	—	5	2	no	—
293	C₂²×D₄	—	5	2	no	—
294	C₂²×D₄	—	10	1	no	—
295	C₂²×D₄	—	10	1	no	—
296	C₂²×D₄	—	10	1	no	—
297	C₂²×D₄	—	10	1	no	—
298	C₂²×D₄	—	10	1	no	—
299	C₂²×D₄	—	10	1	no	—
300	C₂²×D₄	—	10	1	no	—
301	C₂²×D₄	—	10	1	no	—
302	C₂²×D₄	—	10	1	no	—
303	C₂²×D₄	—	10	1	no	—
304	C₂²×D₄	—	10	1	no	—
305	C₂²×D₄	—	10	1	no	—
306	C₂³×C₄	C₂²×D₅	1	1	yes	characteristic
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	—	5	2	no	—
319	C₂×M₁₆	—	5	2	no	—
320	C₂×M₁₆	—	5	2	no	—
321	C₂×M₁₆	—	5	2	no	—
322	C₂×M₁₆	—	5	2	no	—
323	C₂×M₁₆	—	10	1	no	—
324	C₂×M₁₆	—	10	1	no	—
325	C₂×M₁₆	—	10	1	no	—
326	C₂×M₁₆	—	10	1	no	—
327	C₂×M₁₆	—	10	1	no	—
328	C₂×M₁₆	—	10	1	no	—
329	C₂×M₁₆	—	10	1	no	—
330	C₂×M₁₆	—	10	1	no	—
331	C₂×M₁₆	—	10	1	no	—
332	C₂×M₁₆	—	10	1	no	—
333	C₂×M₁₆	—	10	1	no	—
334	C₂×M₁₆	—	10	1	no	—
335	C₂×M₁₆	—	10	1	no	—
336	C₂×M₁₆	D₂₀	1	2	yes	—
337	C₂×M₁₆	D₂₀	1	2	yes	—
338	C₂×M₁₆	C₂²⋊D₅	1	2	yes	—
339	C₂×M₁₆	C₂²⋊D₅	1	2	yes	—
340	C₂×M₁₆	C₂²×D₅	1	2	yes	—
341	C₂×M₁₆	C₂²×D₅	1	2	yes	—
342	C₂×M₁₆	C₂²×D₅	1	2	yes	—
343	C₂²×C₈	—	2	1	no	—
344	C₂²×C₈	—	2	1	no	—
345	C₂²×C₈	—	2	1	no	—
346	C₂²×C₈	—	10	1	no	—
347	C₂²×C₈	—	10	1	no	—
348	C₂²×C₈	—	10	1	no	—
349	#108	—	2	8	no	—
350	#108	—	10	8	no	—
351	#108	—	10	8	no	—
352	#100	—	10	8	no	—
353	#100	—	10	8	no	—
354	#100	—	10	8	no	—
355	C₂²×C₅	—	2	2	no	—
356	C₂²×C₅	—	2	2	no	—
357	C₂²×C₅	—	2	2	no	—
358	C₂²×C₅	—	4	1	no	—
359	C₂²×C₅	—	4	1	no	—
360	C₂²×C₅	—	4	1	no	—
361	C₂²×C₅	—	4	1	no	—
362	C₂²×C₅	#396	1	1	yes	characteristic
363	C₂²×C₅	#396	1	1	yes	characteristic
364	C₂²×C₅	#396	1	1	yes	characteristic
365	C₂²×C₅	#396	1	1	yes	characteristic
366	C₂²×C₅	C₂×C₂²⋊Q₈	1	1	yes	characteristic
367	C₂²×C₅	C₂×C₂²⋊Q₈	1	1	yes	characteristic
368	C₂²×C₅	C₂×C₂²⋊Q₈	1	1	yes	characteristic
369	C₂×D₅	—	4	4	no	—
370	C₂×D₅	—	8	4	no	—
371	C₂×D₅	—	8	4	no	—
372	C₂×D₅	—	8	4	no	—
373	C₂×D₅	—	8	4	no	—
374	C₂×D₅	—	8	4	no	—
375	C₂×D₅	—	8	4	no	—
376	C₂×D₅	—	8	4	no	—
377	C₄×C₅	#396	1	1	yes	characteristic
378	C₄×C₅	#396	1	1	yes	characteristic
379	C₄×C₅	#396	1	1	yes	characteristic
380	C₄×C₅	#396	1	1	yes	characteristic
381	C₄×C₅	C₂×#121	1	1	yes	characteristic
382	C₄×C₅	C₂×#121	1	1	yes	characteristic
383	C₄×C₅	C₂×#121	1	1	yes	characteristic
384	C₄×C₅	C₂×#126	1	1	yes	characteristic
385	C₂⁴	—	5	4	no	—
386	C₂⁴	—	10	2	no	—
387	C₂⁴	—	10	2	no	—
388	C₂⁴	—	10	2	no	—
389	C₂⁴	—	10	2	no	—
390	C₂⁴	—	10	2	no	—
391	C₂⁴	—	10	2	no	—
392	C₂⁴	—	40	4	no	—
393	C₂⁴	Q₈×D₅	1	1	yes	characteristic
394	C₂×D₄	—	10	2	no	—
395	C₂×D₄	—	10	2	no	—
396	C₂×D₄	—	10	2	no	—
397	C₂×D₄	—	10	2	no	—
398	C₂×D₄	—	10	2	no	—
399	C₂×D₄	—	10	2	no	—
400	C₂×D₄	—	10	2	no	—
401	C₂×D₄	—	10	2	no	—
402	C₂×D₄	—	10	2	no	—
403	C₂×D₄	—	10	2	no	—
404	C₂×D₄	—	10	2	no	—
405	C₂×D₄	—	10	2	no	—
406	C₂×D₄	—	20	1	no	—
407	C₂×D₄	—	20	1	no	—
408	C₂×D₄	—	20	1	no	—
409	C₂×D₄	—	20	1	no	—
410	C₂×D₄	—	20	1	no	—
411	C₂×D₄	—	20	1	no	—
412	C₂×D₄	—	20	1	no	—
413	C₂×D₄	—	20	1	no	—
414	C₂×D₄	—	20	1	no	—
415	C₂×D₄	—	20	1	no	—
416	C₂×D₄	—	20	1	no	—
417	C₂×D₄	—	20	1	no	—
418	C₂×D₄	—	20	1	no	—
419	C₂×D₄	—	20	1	no	—
420	C₂×D₄	—	20	1	no	—
421	C₂×D₄	—	20	1	no	—
422	C₂²×C₄	C₂×D₂₀	1	1	yes	characteristic
423	C₂²×C₄	C₂×D₂₀	1	1	yes	characteristic
424	C₂²×C₄	#709	1	1	yes	characteristic
425	C₂²×C₄	#709	1	1	yes	characteristic
426	C₂²×C₄	D₄×D₅	1	1	yes	characteristic
427	C₂²×C₄	D₄×D₅	1	1	yes	characteristic
428	C₂²×C₄	#711	1	1	yes	characteristic
429	C₂²×C₄	#711	1	1	yes	characteristic
430	C₂²×C₄	Q₈×D₅	1	1	yes	characteristic
431	C₂²×C₄	#713	1	1	yes	characteristic
432	C₂²×C₄	#713	1	1	yes	characteristic
433	C₂²×C₄	C₂×C₂²⋊D₅	1	1	yes	characteristic
434	C₂²×C₄	C₂×C₂²⋊D₅	1	1	yes	characteristic
435	C₂²×C₄	C₂³×D₅	1	1	yes	characteristic
436	M₁₆	—	2	2	no	—
437	M₁₆	—	2	2	no	—
438	M₁₆	—	2	2	no	—
439	M₁₆	—	2	2	no	—
440	M₁₆	—	2	2	no	—
441	M₁₆	—	2	2	no	—
442	M₁₆	—	2	2	no	—
443	M₁₆	—	2	2	no	—
444	M₁₆	—	4	1	no	—
445	M₁₆	—	4	1	no	—
446	M₁₆	—	5	4	no	—
447	M₁₆	—	10	2	no	—
448	M₁₆	—	10	2	no	—
449	M₁₆	—	10	2	no	—
450	M₁₆	—	10	2	no	—
451	M₁₆	—	10	2	no	—
452	M₁₆	—	10	2	no	—
453	M₁₆	—	10	2	no	—
454	M₁₆	—	20	1	no	—
455	M₁₆	—	20	1	no	—
456	M₁₆	—	20	1	no	—
457	M₁₆	—	20	1	no	—
458	M₁₆	C₂×D₂₀	1	4	yes	—
459	M₁₆	C₂×C₂²⋊D₅	1	4	yes	—
460	C₂×C₈	—	2	2	no	—
461	C₂×C₈	—	2	2	no	—
462	C₂×C₈	—	2	2	no	—
463	C₂×C₈	—	2	2	no	—
464	C₂×C₈	—	2	2	no	—
465	C₂×C₈	—	2	2	no	—
466	C₂×C₈	—	2	2	no	—
467	C₂×C₈	—	4	1	no	—
468	C₂×C₈	—	4	1	no	—
469	C₂×C₈	—	10	2	no	—
470	C₂×C₈	—	10	2	no	—
471	C₂×C₈	—	10	2	no	—
472	C₂×C₈	—	10	2	no	—
473	C₂×C₈	—	10	2	no	—
474	C₂×C₈	—	20	1	no	—
475	C₂×C₈	—	20	1	no	—
476	C₂×C₈	—	20	1	no	—
477	C₂×C₈	—	20	1	no	—
478	C₂×C₅	—	2	1	no	—
479	C₂×C₅	—	2	1	no	—
480	C₂×C₅	—	2	1	no	—
481	C₂×C₅	—	2	1	no	—
482	C₂×C₅	—	2	1	no	—
483	C₂×C₅	—	2	1	no	—
484	C₂×C₅	#2069	1	2	yes	complemented
485	C₂×C₅	C₂×#396	1	1	yes	characteristic
486	D₅	—	8	4	no	—
487	C₂³	—	4	2	no	—
488	C₂³	—	10	4	no	—
489	C₂³	—	10	4	no	—
490	C₂³	—	10	4	no	—
491	C₂³	—	20	2	no	—
492	C₂³	—	20	2	no	—
493	C₂³	—	20	2	no	—
494	C₂³	—	20	2	no	—
495	C₂³	—	40	4	no	—
496	C₂³	—	40	4	no	—
497	C₂³	—	40	4	no	—
498	C₂³	—	40	4	no	—
499	C₂³	—	40	4	no	—
500	C₂³	—	40	4	no	—
501	C₂³	—	40	4	no	—
502	C₂³	#4042	1	1	yes	characteristic
503	C₂³	#4042	1	1	yes	characteristic
504	C₂³	#4043	1	1	yes	characteristic
505	C₂³	#4043	1	1	yes	characteristic
506	C₂³	#4092	1	1	yes	characteristic
507	C₂³	#4092	1	1	yes	characteristic
508	C₂³	C₂×Q₈×D₅	1	1	yes	characteristic
509	D₄	—	20	2	no	—
510	D₄	—	20	2	no	—
511	D₄	—	20	2	no	—
512	D₄	—	20	2	no	—
513	D₄	—	20	2	no	—
514	D₄	—	20	2	no	—
515	D₄	—	20	2	no	—
516	D₄	—	20	2	no	—
517	C₂×C₄	#4041	1	1	yes	characteristic
518	C₂×C₄	#4041	1	1	yes	characteristic
519	C₂×C₄	#4041	1	1	yes	characteristic
520	C₂×C₄	#4041	1	1	yes	characteristic
521	C₂×C₄	#4042	1	1	yes	characteristic
522	C₂×C₄	#4042	1	1	yes	characteristic
523	C₂×C₄	#4043	1	1	yes	characteristic
524	C₂×C₄	#4043	1	1	yes	characteristic
525	C₂×C₄	#4044	1	1	yes	characteristic
526	C₂×C₄	#4044	1	1	yes	characteristic
527	C₂×C₄	#4044	1	1	yes	characteristic
528	C₂×C₄	#4044	1	1	yes	characteristic
529	C₂×C₄	#4076	1	1	yes	characteristic
530	C₂×C₄	#4076	1	1	yes	characteristic
531	C₂×C₄	#4076	1	1	yes	characteristic
532	C₂×C₄	#4076	1	1	yes	characteristic
533	C₂×C₄	#4085	1	1	yes	characteristic
534	C₂×C₄	#4085	1	1	yes	characteristic
535	C₂×C₄	#4085	1	1	yes	characteristic
536	C₂×C₄	#4085	1	1	yes	characteristic
537	C₂×C₄	#4092	1	1	yes	characteristic
538	C₂×C₄	#4092	1	1	yes	characteristic
539	C₂×C₄	C₂²×D₂₀	1	1	yes	characteristic
540	C₂×C₄	C₂×#709	1	1	yes	characteristic
541	C₂×C₄	C₂×D₄×D₅	1	1	yes	characteristic
542	C₂×C₄	C₂×#711	1	1	yes	characteristic
543	C₂×C₄	C₂×#713	1	1	yes	characteristic
544	C₂×C₄	C₂²×C₂²⋊D₅	1	1	yes	characteristic
545	C₈	—	2	4	no	—
546	C₈	—	2	4	no	—
547	C₈	—	4	2	no	—
548	C₈	—	10	4	no	—
549	C₈	—	20	2	no	—
550	C₈	—	20	2	no	—
551	C₅	C₂×#2069	1	1	yes	characteristic, complemented, Sylow
552	C₂²	—	2	2	no	—
553	C₂²	—	2	2	no	—
554	C₂²	—	2	2	no	—
555	C₂²	—	4	1	no	—
556	C₂²	—	4	1	no	—
557	C₂²	—	4	1	no	—
558	C₂²	—	4	1	no	—
559	C₂²	—	20	4	no	—
560	C₂²	—	40	4	no	—
561	C₂²	—	40	4	no	—
562	C₂²	—	40	4	no	—
563	C₂²	—	40	4	no	—
564	C₂²	—	40	4	no	—
565	C₂²	—	40	4	no	—
566	C₂²	—	40	4	no	—
567	C₂²	#65283	1	1	yes	characteristic
568	C₂²	#65283	1	1	yes	characteristic
569	C₂²	#65283	1	1	yes	characteristic
570	C₂²	#65283	1	1	yes	characteristic
571	C₂²	C₂×#4042	1	1	yes	characteristic
572	C₂²	C₂×#4043	1	1	yes	characteristic
573	C₂²	C₂×#4092	1	1	yes	characteristic
574	C₄	#65283	1	1	yes	characteristic
575	C₄	#65283	1	1	yes	characteristic
576	C₄	#65283	1	1	yes	characteristic
577	C₄	#65283	1	1	yes	characteristic
578	C₄	C₂×#4041	1	1	yes	characteristic
579	C₄	C₂×#4044	1	1	yes	characteristic
580	C₄	C₂×#4076	1	1	yes	characteristic
581	C₄	C₂×#4085	1	1	yes	characteristic
582	C₂	—	2	1	no	—
583	C₂	—	2	1	no	—
584	C₂	—	2	1	no	—
585	C₂	—	2	1	no	—
586	C₂	—	2	1	no	—
587	C₂	—	2	1	no	—
588	C₂	—	40	4	no	—
589	C₂	#10601523	1	2	yes	direct product factor
590	C₂	C₂×#65283	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#65283
commutator, cosocle	C₂²×C₄×C₅	C₂⁴
Frattini	C₂²×C₄	C₂³×D₅
Fitting	C₂×C₅×#430	C₂
socle	C₂²×C₅	#396
prime radical	C₂³×D₂₀	C₂²
hypercenter	C₂×#430	D₅
hypocenter	C₅	C₂×#2069
LCS	G ▷ C₂²×C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂² ◁ C₂³×C₄ ◁ C₂×#430

Complements

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

N	H ≅ G/N	type
1. C₂×C₅×#430	C₂	semidirect
5. C₂×#65414	C₂	semidirect
6. C₂×#65413	C₂	semidirect
7. C₂×#64780	C₂	semidirect
8. #10601523	C₂	direct (N × H)
17. C₅×#430	C₂²	semidirect
29. #65414	C₂²	semidirect
31. #65413	C₂²	semidirect
34. #64780	C₂²	semidirect
102. C₂×#430	D₅	semidirect
213. #430	C₂×D₅	semidirect
484. C₂×C₅	#2069	semidirect
551. C₅	C₂×#2069	semidirect
589. C₂	#10601523	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×#3955	2
C₂×#65414	2
C₂×#65413	2
C₂×#64780	2
#10601523	2
C₂×#2069	5

Subgroups — C2×#10601523 #12128016

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#10601523 #12128016