Subgroups — C₂×#10601511 #12098949

Order 1280.

1314 conjugacy classes of subgroups.

The subgroup lattice has 564 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#4047	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₅×#108	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#65421	C₂	1	2	yes	maximal
4	C₂²×#3951	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#64780	C₂	1	2	yes	maximal, complemented
6	#10601511	C₂	1	8	yes	maximal, direct product factor
7	C₂²×#709	C₂²	1	1	yes	characteristic
8	C₂²×C₅×M₁₆	C₂²	1	2	yes	—
9	C₂³×C₅×C₈	C₂²	1	1	yes	characteristic
10	C₂²×#681	C₂²	1	2	yes	—
11	C₂²×#681	C₂²	1	1	yes	characteristic
12	C₂×#4047	—	2	2	no	—
13	C₂×#4047	—	2	2	no	—
14	C₂×#4047	—	2	2	no	—
15	C₂×#4047	—	2	2	no	—
16	C₂×#4047	C₄	1	4	yes	—
17	C₂×#4047	C₂²	1	4	yes	—
18	C₂²×#676	C₄	1	2	yes	—
19	C₂²×C₈×D₅	C₄	1	2	yes	—
20	C₂×C₅×#108	—	2	2	no	—
21	C₂×C₅×#108	—	2	2	no	—
22	C₂×C₅×#108	C₂²	1	4	yes	complemented
23	C₂×#3956	—	2	2	no	—
24	#65421	—	2	4	no	—
25	#65421	C₂²	1	8	yes	—
26	C₂×#3955	—	2	2	no	—
27	C₂×#3951	—	2	2	no	—
28	C₂×#3951	—	2	2	no	—
29	C₂×#3951	C₂²	1	4	yes	complemented
30	#64780	C₂²	1	8	yes	complemented
31	C₂×#1813	—	5	1	no	maximal, Sylow
32	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
33	C₂²×C₂²⋊D₅	Q₈	1	2	yes	—
34	C₂×#709	—	2	1	no	—
35	C₂×#709	—	2	1	no	—
36	C₂×#709	—	2	1	no	—
37	C₂×#709	—	2	1	no	—
38	C₂×#709	—	2	1	no	—
39	C₂×#709	—	2	1	no	—
40	C₂×#709	—	2	1	no	—
41	C₂×#709	—	2	1	no	—
42	C₂×#709	C₂×C₄	1	2	yes	—
43	C₂×#709	D₄	1	2	yes	—
44	C₂×#709	Q₈	1	2	yes	—
45	C₂×#709	C₂³	1	2	yes	—
46	C₂²×D₂₀	D₄	1	1	yes	characteristic
47	C₂²×C₄×D₅	C₂×C₄	1	2	yes	—
48	C₂²×Dic₁₀	D₄	1	1	yes	characteristic
49	C₂×C₅×M₁₆	—	2	2	no	—
50	C₂×C₅×M₁₆	—	2	2	no	—
51	C₂×C₅×M₁₆	—	2	2	no	—
52	C₂×C₅×M₁₆	—	2	2	no	—
53	C₂×C₅×M₁₆	—	2	2	no	—
54	C₂×C₅×M₁₆	C₂³	1	4	yes	—
55	C₂²×C₅×C₈	—	2	2	no	—
56	C₂²×C₅×C₈	C₂×C₄	1	1	yes	characteristic
57	C₂²×C₅×C₈	C₂×C₄	1	1	yes	characteristic
58	C₂²×C₅×C₈	C₂×C₄	1	2	yes	—
59	C₂²×C₅×C₈	D₄	1	2	yes	—
60	C₂²×C₅×C₈	D₄	1	2	yes	—
61	C₂²×C₅×C₈	D₄	1	2	yes	—
62	C₂²×C₅×C₈	D₄	1	2	yes	—
63	C₂²×C₅×C₈	C₂³	1	2	yes	—
64	C₂×#681	—	2	1	no	—
65	C₂×#681	—	2	1	no	—
66	C₂×#681	—	2	1	no	—
67	C₂×#681	—	2	1	no	—
68	C₂×#681	—	2	2	no	—
69	C₂×#681	—	2	2	no	—
70	C₂×#681	—	2	2	no	—
71	C₂×#681	—	2	2	no	—
72	C₂×#681	—	2	2	no	—
73	C₂×#681	C₂×C₄	1	2	yes	—
74	C₂×#681	C₂³	1	4	yes	—
75	C₂×#681	C₂³	1	2	yes	—
76	C₂²×#168	—	2	2	no	—
77	C₂²×#168	C₂×C₄	1	2	yes	—
78	#4047	—	2	8	no	—
79	#4047	—	2	8	no	—
80	#4047	—	2	8	no	—
81	#4047	—	2	8	no	—
82	C₂×#676	—	2	4	no	—
83	C₂×#676	—	2	4	no	—
84	C₂×#676	C₂×C₄	1	8	yes	—
85	C₂×C₈×D₅	—	2	4	no	—
86	C₂×C₈×D₅	—	2	4	no	—
87	C₂×C₈×D₅	C₂×C₄	1	8	yes	—
88	C₅×#108	—	2	8	no	—
89	#3956	—	2	8	no	—
90	#3955	—	2	8	no	—
91	#3951	—	2	8	no	—
92	C₂²×#131	—	5	1	no	—
93	C₂²×#108	—	5	1	no	—
94	C₂²×#108	D₅	1	1	yes	characteristic, complemented
95	C₂×#413	—	5	2	no	—
96	#1813	—	5	8	no	—
97	C₂×#338	—	5	2	no	—
98	C₂⁴×C₅	C₂×Q₈	1	1	yes	characteristic
99	C₂³×D₅	C₄⋊C₄	1	2	yes	—
100	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
101	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
102	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
103	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
104	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
105	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
106	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
107	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
108	C₂²×C₄×C₅	C₂×Q₈	1	1	yes	characteristic
109	C₂²×C₄×C₅	#41	1	1	yes	characteristic
110	C₂²×C₄×C₅	#41	1	1	yes	characteristic
111	C₂²×C₄×C₅	#41	1	1	yes	characteristic
112	C₂²×C₄×C₅	#41	1	1	yes	characteristic
113	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
114	C₂×C₂²⋊D₅	—	2	2	no	—
115	C₂×C₂²⋊D₅	—	2	2	no	—
116	C₂×C₂²⋊D₅	—	2	2	no	—
117	C₂×C₂²⋊D₅	—	2	2	no	—
118	C₂×C₂²⋊D₅	C₄⋊C₄	1	4	yes	—
119	C₂×C₂²⋊D₅	C₂×Q₈	1	4	yes	—
120	C₂²×Dic₅	C₄⋊C₄	1	2	yes	—
121	#709	—	2	2	no	—
122	#709	—	2	2	no	—
123	#709	—	2	2	no	—
124	#709	—	2	2	no	—
125	#709	—	2	2	no	—
126	#709	—	2	2	no	—
127	#709	—	2	2	no	—
128	#709	—	2	2	no	—
129	#709	—	2	2	no	—
130	#709	—	2	2	no	—
131	#709	—	2	2	no	—
132	#709	—	2	2	no	—
133	#709	—	2	2	no	—
134	#709	—	2	2	no	—
135	#709	—	2	2	no	—
136	#709	—	2	2	no	—
137	C₂×D₂₀	—	2	1	no	—
138	C₂×D₂₀	—	2	1	no	—
139	C₂×D₂₀	—	2	1	no	—
140	C₂×D₂₀	—	2	1	no	—
141	C₂×D₂₀	C₄⋊C₄	1	2	yes	—
142	C₂×D₂₀	C₂×D₄	1	2	yes	—
143	C₂×C₄×D₅	—	2	2	no	—
144	C₂×C₄×D₅	—	2	2	no	—
145	C₂×C₄×D₅	—	2	2	no	—
146	C₂×C₄×D₅	—	2	2	no	—
147	C₂×C₄×D₅	C₄⋊C₄	1	4	yes	—
148	C₂×C₄×D₅	C₂²×C₄	1	4	yes	—
149	C₂×Dic₁₀	—	2	1	no	—
150	C₂×Dic₁₀	—	2	1	no	—
151	C₂×Dic₁₀	—	2	1	no	—
152	C₂×Dic₁₀	—	2	1	no	—
153	C₂×Dic₁₀	C₄⋊C₄	1	2	yes	—
154	C₂×Dic₁₀	C₂×D₄	1	2	yes	—
155	C₅×M₁₆	—	2	4	no	—
156	C₅×M₁₆	—	2	4	no	—
157	C₅×M₁₆	—	4	2	no	—
158	C₅×M₁₆	—	4	2	no	—
159	C₂×C₅×C₈	—	2	4	no	—
160	C₂×C₅×C₈	—	4	2	no	—
161	C₂×C₅×C₈	—	4	2	no	—
162	C₂×C₅×C₈	C₂²⋊C₄	1	2	yes	—
163	C₂×C₅×C₈	C₂²⋊C₄	1	2	yes	—
164	C₂×C₅×C₈	C₂²⋊C₄	1	2	yes	—
165	C₂×C₅×C₈	C₂²⋊C₄	1	2	yes	—
166	C₂×C₅×C₈	C₂²⋊C₄	1	4	yes	—
167	C₂×C₅×C₈	C₂²⋊C₄	1	4	yes	—
168	C₂×C₅×C₈	C₂²×C₄	1	2	yes	—
169	C₂×C₅×C₈	C₂²×C₄	1	2	yes	—
170	C₂×C₅×C₈	C₂×D₄	1	4	yes	—
171	C₂×C₅×C₈	C₂×D₄	1	4	yes	—
172	#681	—	2	2	no	—
173	#681	—	2	2	no	—
174	#681	—	2	2	no	—
175	#681	—	2	2	no	—
176	#681	—	2	4	no	—
177	#681	—	2	4	no	—
178	#681	—	4	2	no	—
179	#681	—	4	2	no	—
180	C₂×#168	—	2	2	no	—
181	C₂×#168	—	2	2	no	—
182	C₂×#168	—	2	4	no	—
183	C₂×#168	—	4	2	no	—
184	C₂×#168	—	4	2	no	—
185	C₂×#168	C₂²×C₄	1	4	yes	—
186	#676	—	2	16	no	—
187	C₈×D₅	—	2	16	no	—
188	C₂²×#41	—	5	1	no	—
189	C₂×#131	—	5	4	no	—
190	C₂×#131	—	5	4	no	—
191	C₂×#131	—	10	2	no	—
192	C₂×#131	—	10	2	no	—
193	C₂×#131	—	10	2	no	—
194	C₂×#131	—	10	2	no	—
195	C₂²×M₁₆	—	5	1	no	—
196	C₂²×M₁₆	—	5	2	no	—
197	C₂²×M₁₆	—	5	2	no	—
198	C₂²×M₁₆	C₂×D₅	1	2	yes	—
199	C₂³×C₈	—	5	2	no	—
200	C₂³×C₈	C₂×D₅	1	1	yes	characteristic
201	C₂×#108	—	2	2	no	—
202	C₂×#108	—	2	2	no	—
203	C₂×#108	—	5	4	no	—
204	C₂×#108	—	10	2	no	—
205	C₂×#108	—	10	2	no	—
206	C₂×#108	C₂×D₅	1	4	yes	complemented
207	#413	—	5	8	no	—
208	#413	—	10	4	no	—
209	C₂×#101	—	10	2	no	—
210	C₂×#100	—	10	2	no	—
211	#338	—	5	8	no	—
212	C₂³×C₅	—	4	2	no	—
213	C₂³×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
214	C₂³×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
215	C₂³×C₅	C₂²⋊Q₈	1	1	yes	characteristic
216	C₂³×C₅	C₂²⋊Q₈	1	1	yes	characteristic
217	C₂³×C₅	C₂²⋊Q₈	1	1	yes	characteristic
218	C₂³×C₅	C₂²⋊Q₈	1	1	yes	characteristic
219	C₂³×C₅	C₂²×Q₈	1	1	yes	characteristic
220	C₂²×D₅	—	2	2	no	—
221	C₂²×D₅	—	2	2	no	—
222	C₂²×D₅	—	4	4	no	—
223	C₂²×D₅	C₂×C₄⋊C₄	1	4	yes	—
224	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
225	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
226	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
227	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
228	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
229	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
230	C₂×C₄×C₅	#117	1	1	yes	characteristic
231	C₂×C₄×C₅	#117	1	1	yes	characteristic
232	C₂×C₄×C₅	#117	1	1	yes	characteristic
233	C₂×C₄×C₅	#117	1	1	yes	characteristic
234	C₂×C₄×C₅	#121	1	1	yes	characteristic
235	C₂×C₄×C₅	#121	1	1	yes	characteristic
236	C₂×C₄×C₅	#121	1	1	yes	characteristic
237	C₂×C₄×C₅	#121	1	1	yes	characteristic
238	C₂×C₄×C₅	#121	1	1	yes	characteristic
239	C₂×C₄×C₅	#121	1	1	yes	characteristic
240	C₂×C₄×C₅	#121	1	1	yes	characteristic
241	C₂×C₄×C₅	#121	1	1	yes	characteristic
242	C₂×C₄×C₅	C₂²⋊Q₈	1	1	yes	characteristic
243	C₂×C₄×C₅	C₂²⋊Q₈	1	1	yes	characteristic
244	C₂×C₄×C₅	C₂²⋊Q₈	1	1	yes	characteristic
245	C₂×C₄×C₅	C₂²⋊Q₈	1	1	yes	characteristic
246	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
247	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
248	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
249	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
250	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
251	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
252	C₂²⋊D₅	—	2	4	no	—
253	C₂²⋊D₅	—	2	4	no	—
254	C₂²⋊D₅	—	2	4	no	—
255	C₂²⋊D₅	—	2	4	no	—
256	C₂×Dic₅	—	2	2	no	—
257	C₂×Dic₅	—	2	2	no	—
258	C₂×Dic₅	C₂×C₄⋊C₄	1	4	yes	—
259	D₂₀	—	2	2	no	—
260	D₂₀	—	2	2	no	—
261	D₂₀	—	2	2	no	—
262	D₂₀	—	2	2	no	—
263	C₄×D₅	—	2	4	no	—
264	C₄×D₅	—	2	4	no	—
265	C₄×D₅	—	2	4	no	—
266	C₄×D₅	—	2	4	no	—
267	Dic₁₀	—	2	2	no	—
268	Dic₁₀	—	2	2	no	—
269	Dic₁₀	—	2	2	no	—
270	Dic₁₀	—	2	2	no	—
271	C₅×C₈	—	4	4	no	—
272	C₅×C₈	C₂×C₂²⋊C₄	1	4	yes	—
273	C₅×C₈	C₂×C₂²⋊C₄	1	4	yes	—
274	#168	—	2	4	no	—
275	#168	—	4	4	no	—
276	C₂×#41	—	5	2	no	—
277	C₂×#41	—	5	2	no	—
278	C₂×#41	—	5	2	no	—
279	C₂×#41	—	5	2	no	—
280	C₂×#41	—	10	1	no	—
281	C₂×#41	—	10	1	no	—
282	C₂×#41	—	10	1	no	—
283	C₂×#41	—	10	1	no	—
284	C₂×#41	—	10	1	no	—
285	C₂×#41	—	10	1	no	—
286	C₂×#41	—	10	1	no	—
287	C₂×#41	—	10	1	no	—
288	C₂²×Q₈	—	5	1	no	—
289	C₂²×D₄	—	5	2	no	—
290	C₂²×D₄	—	5	1	no	—
291	C₂³×C₄	—	5	2	no	—
292	C₂³×C₄	C₂²×D₅	1	1	yes	characteristic
293	#131	—	10	8	no	—
294	#131	—	10	8	no	—
295	#131	—	10	8	no	—
296	#131	—	10	8	no	—
297	C₂×M₁₆	—	2	2	no	—
298	C₂×M₁₆	—	2	2	no	—
299	C₂×M₁₆	—	2	2	no	—
300	C₂×M₁₆	—	2	2	no	—
301	C₂×M₁₆	—	2	2	no	—
302	C₂×M₁₆	—	5	2	no	—
303	C₂×M₁₆	—	5	2	no	—
304	C₂×M₁₆	—	5	8	no	—
305	C₂×M₁₆	—	5	4	no	—
306	C₂×M₁₆	—	10	1	no	—
307	C₂×M₁₆	—	10	1	no	—
308	C₂×M₁₆	—	10	1	no	—
309	C₂×M₁₆	—	10	1	no	—
310	C₂×M₁₆	—	10	2	no	—
311	C₂×M₁₆	—	10	4	no	—
312	C₂×M₁₆	—	10	4	no	—
313	C₂×M₁₆	—	10	2	no	—
314	C₂×M₁₆	—	10	2	no	—
315	C₂×M₁₆	—	10	2	no	—
316	C₂×M₁₆	—	10	2	no	—
317	C₂×M₁₆	C₂²×D₅	1	4	yes	—
318	C₂²×C₈	—	2	2	no	—
319	C₂²×C₈	—	5	2	no	—
320	C₂²×C₈	—	5	8	no	—
321	C₂²×C₈	—	10	4	no	—
322	C₂²×C₈	—	10	4	no	—
323	C₂²×C₈	—	10	2	no	—
324	C₂²×C₈	C₄×D₅	1	1	yes	characteristic
325	C₂²×C₈	C₄×D₅	1	1	yes	characteristic
326	C₂²×C₈	C₄×D₅	1	2	yes	—
327	C₂²×C₈	D₂₀	1	2	yes	—
328	C₂²×C₈	D₂₀	1	2	yes	—
329	C₂²×C₈	C₂²⋊D₅	1	2	yes	—
330	C₂²×C₈	C₂²⋊D₅	1	2	yes	—
331	C₂²×C₈	C₂²×D₅	1	2	yes	—
332	#108	—	2	8	no	—
333	#108	—	10	8	no	—
334	#101	—	10	8	no	—
335	#100	—	10	8	no	—
336	C₂²×C₅	—	2	2	no	—
337	C₂²×C₅	—	2	2	no	—
338	C₂²×C₅	—	2	2	no	—
339	C₂²×C₅	—	4	1	no	—
340	C₂²×C₅	—	4	1	no	—
341	C₂²×C₅	—	4	1	no	—
342	C₂²×C₅	—	4	1	no	—
343	C₂²×C₅	#380	1	1	yes	characteristic
344	C₂²×C₅	#380	1	1	yes	characteristic
345	C₂²×C₅	#380	1	1	yes	characteristic
346	C₂²×C₅	#380	1	1	yes	characteristic
347	C₂²×C₅	C₂²×C₄⋊C₄	1	1	yes	characteristic
348	C₂²×C₅	C₂×C₂²⋊Q₈	1	1	yes	characteristic
349	C₂²×C₅	C₂×C₂²⋊Q₈	1	1	yes	characteristic
350	C₂×D₅	—	2	4	no	—
351	C₂×D₅	—	4	4	no	—
352	C₂×D₅	—	4	4	no	—
353	C₂×D₅	—	4	4	no	—
354	C₄×C₅	#380	1	1	yes	characteristic
355	C₄×C₅	#380	1	1	yes	characteristic
356	C₄×C₅	#380	1	1	yes	characteristic
357	C₄×C₅	#380	1	1	yes	characteristic
358	C₄×C₅	C₂²×C₂²⋊C₄	1	1	yes	characteristic
359	C₄×C₅	C₂×#117	1	1	yes	characteristic
360	C₄×C₅	C₂×#121	1	1	yes	characteristic
361	C₄×C₅	C₂×#121	1	1	yes	characteristic
362	Dic₅	—	2	4	no	—
363	C₂⁴	—	5	2	no	—
364	C₂⁴	Q₈×D₅	1	1	yes	characteristic
365	#41	—	10	2	no	—
366	#41	—	10	2	no	—
367	#41	—	10	2	no	—
368	#41	—	10	2	no	—
369	#41	—	10	2	no	—
370	#41	—	10	2	no	—
371	#41	—	10	2	no	—
372	#41	—	10	2	no	—
373	#41	—	10	2	no	—
374	#41	—	10	2	no	—
375	#41	—	10	2	no	—
376	#41	—	10	2	no	—
377	#41	—	10	2	no	—
378	#41	—	10	2	no	—
379	#41	—	10	2	no	—
380	#41	—	10	2	no	—
381	C₂×Q₈	—	5	2	no	—
382	C₂×Q₈	—	5	2	no	—
383	C₂×Q₈	—	10	1	no	—
384	C₂×Q₈	—	10	1	no	—
385	C₂×Q₈	—	10	1	no	—
386	C₂×Q₈	—	10	1	no	—
387	C₂×D₄	—	5	4	no	—
388	C₂×D₄	—	5	4	no	—
389	C₂×D₄	—	5	2	no	—
390	C₂×D₄	—	5	2	no	—
391	C₂×D₄	—	10	2	no	—
392	C₂×D₄	—	10	2	no	—
393	C₂×D₄	—	10	2	no	—
394	C₂×D₄	—	10	2	no	—
395	C₂×D₄	—	10	1	no	—
396	C₂×D₄	—	10	1	no	—
397	C₂×D₄	—	10	1	no	—
398	C₂×D₄	—	10	1	no	—
399	C₂²×C₄	—	5	2	no	—
400	C₂²×C₄	—	5	4	no	—
401	C₂²×C₄	—	5	4	no	—
402	C₂²×C₄	—	10	2	no	—
403	C₂²×C₄	—	10	2	no	—
404	C₂²×C₄	—	10	2	no	—
405	C₂²×C₄	—	10	2	no	—
406	C₂²×C₄	C₂×C₄×D₅	1	1	yes	characteristic
407	C₂²×C₄	C₂×C₄×D₅	1	1	yes	characteristic
408	C₂²×C₄	C₂×D₂₀	1	1	yes	characteristic
409	C₂²×C₄	C₂×D₂₀	1	1	yes	characteristic
410	C₂²×C₄	D₄×D₅	1	1	yes	characteristic
411	C₂²×C₄	D₄×D₅	1	1	yes	characteristic
412	C₂²×C₄	#711	1	1	yes	characteristic
413	C₂²×C₄	#711	1	1	yes	characteristic
414	C₂²×C₄	Q₈×D₅	1	1	yes	characteristic
415	C₂²×C₄	#713	1	1	yes	characteristic
416	C₂²×C₄	#713	1	1	yes	characteristic
417	C₂²×C₄	C₂×C₂²⋊D₅	1	1	yes	characteristic
418	C₂²×C₄	C₂×C₂²⋊D₅	1	1	yes	characteristic
419	C₂²×C₄	C₂³×D₅	1	1	yes	characteristic
420	M₁₆	—	2	4	no	—
421	M₁₆	—	2	4	no	—
422	M₁₆	—	4	2	no	—
423	M₁₆	—	4	2	no	—
424	M₁₆	—	10	2	no	—
425	M₁₆	—	10	2	no	—
426	M₁₆	—	10	2	no	—
427	M₁₆	—	10	2	no	—
428	M₁₆	—	10	16	no	—
429	M₁₆	—	10	4	no	—
430	M₁₆	—	10	4	no	—
431	M₁₆	—	20	2	no	—
432	M₁₆	—	20	2	no	—
433	C₂×C₈	—	2	4	no	—
434	C₂×C₈	—	4	2	no	—
435	C₂×C₈	—	4	2	no	—
436	C₂×C₈	—	5	4	no	—
437	C₂×C₈	—	10	2	no	—
438	C₂×C₈	—	10	2	no	—
439	C₂×C₈	—	10	16	no	—
440	C₂×C₈	—	10	4	no	—
441	C₂×C₈	—	20	2	no	—
442	C₂×C₈	—	20	2	no	—
443	C₂×C₈	#685	1	2	yes	—
444	C₂×C₈	#685	1	2	yes	—
445	C₂×C₈	#685	1	2	yes	—
446	C₂×C₈	#685	1	2	yes	—
447	C₂×C₈	#685	1	4	yes	—
448	C₂×C₈	#685	1	4	yes	—
449	C₂×C₈	C₂×C₄×D₅	1	2	yes	—
450	C₂×C₈	C₂×C₄×D₅	1	2	yes	—
451	C₂×C₈	C₂×D₂₀	1	4	yes	—
452	C₂×C₈	C₂×C₂²⋊D₅	1	4	yes	—
453	C₂×C₅	—	2	1	no	—
454	C₂×C₅	—	2	1	no	—
455	C₂×C₅	—	2	1	no	—
456	C₂×C₅	—	2	1	no	—
457	C₂×C₅	—	2	1	no	—
458	C₂×C₅	—	2	1	no	—
459	C₂×C₅	#1813	1	2	yes	complemented
460	C₂×C₅	C₂×#380	1	1	yes	characteristic
461	D₅	—	4	4	no	—
462	C₂³	—	4	2	no	—
463	C₂³	—	5	4	no	—
464	C₂³	—	10	2	no	—
465	C₂³	—	10	2	no	—
466	C₂³	—	20	4	no	—
467	C₂³	D₅×C₄⋊C₄	1	1	yes	characteristic
468	C₂³	D₅×C₄⋊C₄	1	1	yes	characteristic
469	C₂³	#4043	1	1	yes	characteristic
470	C₂³	#4043	1	1	yes	characteristic
471	C₂³	#4092	1	1	yes	characteristic
472	C₂³	#4092	1	1	yes	characteristic
473	C₂³	C₂×Q₈×D₅	1	1	yes	characteristic
474	Q₈	—	10	2	no	—
475	Q₈	—	10	2	no	—
476	Q₈	—	10	2	no	—
477	Q₈	—	10	2	no	—
478	D₄	—	10	4	no	—
479	D₄	—	10	4	no	—
480	D₄	—	10	4	no	—
481	D₄	—	10	4	no	—
482	D₄	—	10	2	no	—
483	D₄	—	10	2	no	—
484	D₄	—	10	2	no	—
485	D₄	—	10	2	no	—
486	C₂×C₄	—	5	4	no	—
487	C₂×C₄	—	10	2	no	—
488	C₂×C₄	—	10	2	no	—
489	C₂×C₄	—	10	4	no	—
490	C₂×C₄	—	10	4	no	—
491	C₂×C₄	—	10	4	no	—
492	C₂×C₄	—	10	4	no	—
493	C₂×C₄	D₅×C₄⋊C₄	1	1	yes	characteristic
494	C₂×C₄	D₅×C₄⋊C₄	1	1	yes	characteristic
495	C₂×C₄	#4038	1	1	yes	characteristic
496	C₂×C₄	#4038	1	1	yes	characteristic
497	C₂×C₄	#4038	1	1	yes	characteristic
498	C₂×C₄	#4038	1	1	yes	characteristic
499	C₂×C₄	#4041	1	1	yes	characteristic
500	C₂×C₄	#4041	1	1	yes	characteristic
501	C₂×C₄	#4041	1	1	yes	characteristic
502	C₂×C₄	#4041	1	1	yes	characteristic
503	C₂×C₄	#4043	1	1	yes	characteristic
504	C₂×C₄	#4043	1	1	yes	characteristic
505	C₂×C₄	C₂×#685	1	1	yes	characteristic
506	C₂×C₄	C₂×#685	1	1	yes	characteristic
507	C₂×C₄	C₂×#685	1	1	yes	characteristic
508	C₂×C₄	C₂×#685	1	1	yes	characteristic
509	C₂×C₄	#4084	1	1	yes	characteristic
510	C₂×C₄	#4084	1	1	yes	characteristic
511	C₂×C₄	#4084	1	1	yes	characteristic
512	C₂×C₄	#4084	1	1	yes	characteristic
513	C₂×C₄	#4092	1	1	yes	characteristic
514	C₂×C₄	#4092	1	1	yes	characteristic
515	C₂×C₄	C₂²×C₄×D₅	1	1	yes	characteristic
516	C₂×C₄	C₂²×D₂₀	1	1	yes	characteristic
517	C₂×C₄	C₂×D₄×D₅	1	1	yes	characteristic
518	C₂×C₄	C₂×#711	1	1	yes	characteristic
519	C₂×C₄	C₂×#713	1	1	yes	characteristic
520	C₂×C₄	C₂²×C₂²⋊D₅	1	1	yes	characteristic
521	C₈	—	4	4	no	—
522	C₈	—	10	4	no	—
523	C₈	—	20	4	no	—
524	C₈	C₂×#685	1	4	yes	—
525	C₈	C₂×#685	1	4	yes	—
526	C₅	C₂×#1813	1	1	yes	characteristic, complemented, Sylow
527	C₂²	—	2	2	no	—
528	C₂²	—	2	2	no	—
529	C₂²	—	2	2	no	—
530	C₂²	—	4	1	no	—
531	C₂²	—	4	1	no	—
532	C₂²	—	4	1	no	—
533	C₂²	—	4	1	no	—
534	C₂²	—	10	4	no	—
535	C₂²	—	20	4	no	—
536	C₂²	—	20	4	no	—
537	C₂²	—	20	4	no	—
538	C₂²	#65276	1	1	yes	characteristic
539	C₂²	#65276	1	1	yes	characteristic
540	C₂²	#65276	1	1	yes	characteristic
541	C₂²	#65276	1	1	yes	characteristic
542	C₂²	C₂×D₅×C₄⋊C₄	1	1	yes	characteristic
543	C₂²	C₂×#4043	1	1	yes	characteristic
544	C₂²	C₂×#4092	1	1	yes	characteristic
545	C₄	—	10	4	no	—
546	C₄	#65276	1	1	yes	characteristic
547	C₄	#65276	1	1	yes	characteristic
548	C₄	#65276	1	1	yes	characteristic
549	C₄	#65276	1	1	yes	characteristic
550	C₄	C₂×#4038	1	1	yes	characteristic
551	C₄	C₂×#4041	1	1	yes	characteristic
552	C₄	C₂²×#685	1	1	yes	characteristic
553	C₄	C₂×#4084	1	1	yes	characteristic
554	C₂	—	2	1	no	—
555	C₂	—	2	1	no	—
556	C₂	—	2	1	no	—
557	C₂	—	2	1	no	—
558	C₂	—	2	1	no	—
559	C₂	—	2	1	no	—
560	C₂	—	20	4	no	—
561	C₂	#10601511	1	2	yes	direct product factor
562	C₂	C₂×#65276	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	#4038
commutator	C₂×C₄×C₅	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₅
Fitting	C₂²×C₅×#108	C₂
socle	C₂²×C₅	#380
prime radical	C₂²×#709	C₂²
cosocle	C₂²×C₄×C₅	C₂⁴
hypercenter	C₂²×#108	D₅
hypocenter	C₅	C₂×#1813
LCS	G ▷ C₂×C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₄ ◁ C₂³×C₄ ◁ C₂²×#108

Complements

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

N	H ≅ G/N	type
2. C₂²×C₅×#108	C₂	semidirect
4. C₂²×#3951	C₂	semidirect
5. C₂×#64780	C₂	semidirect
6. #10601511	C₂	direct (N × H)
22. C₂×C₅×#108	C₂²	semidirect
29. C₂×#3951	C₂²	semidirect
30. #64780	C₂²	semidirect
94. C₂²×#108	D₅	semidirect
206. C₂×#108	C₂×D₅	semidirect
459. C₂×C₅	#1813	semidirect
526. C₅	C₂×#1813	semidirect
561. C₂	#10601511	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×#4047	2
C₂²×C₅×#108	2
C₂×#65421	2
C₂²×#3951	2
C₂×#64780	2
#10601511	2
C₂×#1813	5

Subgroups — C2×#10601511 #12098949

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#10601511 #12098949