Subgroups — #12104235

Order 1280.

780 conjugacy classes of subgroups.

The subgroup lattice has 526 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#10610769	C₂	1	1	yes	maximal, characteristic
2	C₂×#65122	C₂	1	1	yes	maximal, characteristic
3	C₄×D₅×M₁₆	C₂	1	1	yes	maximal, characteristic
4	C₅×#1950	C₂	1	1	yes	maximal, characteristic, complemented
5	#10601506	C₂	1	2	yes	maximal
6	Dic₅×#108	C₂	1	2	yes	maximal, complemented
7	#10601313	C₂	1	1	yes	maximal, characteristic, complemented
8	#10601267	C₂	1	1	yes	maximal, characteristic, complemented
9	#10600668	C₂	1	1	yes	maximal, characteristic, complemented
10	#10599734	C₂	1	2	yes	maximal
11	#10599709	C₂	1	2	yes	maximal, complemented
12	C₂×D₅×M₁₆	C₂²	1	1	yes	characteristic
13	C₂×D₅×M₁₆	C₂²	1	1	yes	characteristic
14	C₂×C₄²×D₅	C₂²	1	1	yes	characteristic
15	C₂×C₅×#108	C₂²	1	2	yes	—
16	C₅×#423	C₂²	1	1	yes	characteristic
17	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
18	C₄×C₅×M₁₆	C₂²	1	1	yes	characteristic
19	#65415	C₂²	1	2	yes	—
20	C₂×#3954	C₂²	1	2	yes	—
21	C₂×#3954	C₂²	1	2	yes	—
22	M₁₆×Dic₅	C₂²	1	1	yes	characteristic
23	M₁₆×Dic₅	C₂²	1	2	yes	—
24	M₁₆×Dic₅	C₂²	1	1	yes	characteristic
25	C₂×#3952	C₂²	1	2	yes	—
26	C₂×#3951	C₂²	1	2	yes	—
27	C₂×C₈×Dic₅	C₂²	1	2	yes	—
28	#65213	C₂²	1	1	yes	characteristic
29	C₂×C₄⋊#168	C₂²	1	1	yes	characteristic
30	C₄×#681	C₂²	1	1	yes	characteristic
31	#65124	—	2	1	no	—
32	#65124	—	2	1	no	—
33	#65122	—	2	1	no	—
34	#65122	—	2	1	no	—
35	#65122	C₄	1	2	yes	—
36	#65122	C₄	1	2	yes	—
37	#65122	C₄	1	2	yes	—
38	#65122	C₄	1	2	yes	—
39	#64996	—	2	1	no	—
40	D₅×#97	—	2	1	no	—
41	C₄×#676	—	2	1	no	—
42	C₄×C₈×D₅	—	2	1	no	—
43	C₅×#341	C₂²	1	2	yes	—
44	#64778	C₂²	1	2	yes	—
45	#64778	C₂²	1	2	yes	—
46	#64772	C₂²	1	2	yes	—
47	#21370	—	5	1	no	maximal, Sylow
48	C₂²×C₄×D₅	Q₈	1	1	yes	characteristic
49	C₂²×C₄×D₅	Q₈	1	1	yes	characteristic
50	C₂²×C₄×D₅	C₂³	1	1	yes	characteristic
51	C₂×C₅×M₁₆	C₂³	1	2	yes	—
52	C₂×C₅×M₁₆	C₂³	1	1	yes	characteristic
53	C₂×C₅×M₁₆	C₂³	1	1	yes	characteristic
54	C₂²×C₅×C₈	C₂³	1	2	yes	—
55	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
56	C₂×C₄×Dic₅	Q₈	1	1	yes	characteristic
57	C₂×C₄×Dic₅	Q₈	1	1	yes	characteristic
58	C₂×C₄×Dic₅	C₂³	1	1	yes	characteristic
59	C₂×#681	C₂³	1	2	yes	—
60	C₂×#681	C₂³	1	1	yes	characteristic
61	C₂×#681	C₂³	1	1	yes	characteristic
62	C₂²×#168	C₂³	1	2	yes	—
63	D₅×M₁₆	—	2	2	no	—
64	D₅×M₁₆	—	2	2	no	—
65	D₅×M₁₆	—	2	2	no	—
66	D₅×M₁₆	—	2	2	no	—
67	C₂×#676	—	2	1	no	—
68	C₂×#676	—	2	1	no	—
69	C₂×C₈×D₅	—	2	1	no	—
70	C₂×C₈×D₅	—	2	1	no	—
71	C₄²×D₅	C₂×C₄	1	1	yes	characteristic
72	C₄²×D₅	C₂×C₄	1	1	yes	characteristic
73	C₄²×D₅	C₂×C₄	1	1	yes	characteristic
74	C₄²×D₅	C₂×C₄	1	1	yes	characteristic
75	C₄²×D₅	D₄	1	1	yes	characteristic
76	C₄²×D₅	D₄	1	1	yes	characteristic
77	C₄²×D₅	D₄	1	1	yes	characteristic
78	C₄²×D₅	D₄	1	1	yes	characteristic
79	C₅×#108	—	2	4	no	—
80	C₅×C₄⋊C₈	—	2	1	no	—
81	C₅×C₄⋊C₈	—	2	1	no	—
82	C₅×C₄⋊C₈	C₂×C₄	1	2	yes	—
83	C₅×C₄⋊C₈	C₂×C₄	1	2	yes	—
84	C₅×#97	—	2	1	no	—
85	C₄×C₅×C₈	—	2	1	no	—
86	#3954	—	2	4	no	—
87	#3954	—	2	4	no	—
88	#3952	—	2	2	no	—
89	#3952	—	2	2	no	—
90	#3952	C₂×C₄	1	4	yes	—
91	#3952	C₂×C₄	1	4	yes	—
92	#3951	—	2	4	no	—
93	#3947	—	2	2	no	—
94	#3947	—	2	1	no	—
95	#3947	—	2	1	no	—
96	C₈×Dic₅	—	2	2	no	—
97	C₈×Dic₅	—	2	1	no	—
98	C₈×Dic₅	—	2	1	no	—
99	C₈×Dic₅	C₂×C₄	1	4	yes	—
100	C₈×Dic₅	C₂×C₄	1	4	yes	—
101	C₄⋊#168	—	2	1	no	—
102	C₄⋊#168	—	2	1	no	—
103	C₄⋊#168	C₂×C₄	1	2	yes	—
104	C₄⋊#168	C₂×C₄	1	2	yes	—
105	#3935	—	2	1	no	—
106	C₄×#168	—	2	1	no	—
107	#2920	—	5	1	no	—
108	C₂×#431	—	5	1	no	—
109	C₂×C₄×M₁₆	—	5	1	no	—
110	#1950	—	5	1	no	—
111	#1950	—	5	1	no	—
112	#1950	—	5	1	no	—
113	#1950	D₅	1	1	yes	characteristic, complemented
114	#1855	—	5	2	no	—
115	#1855	—	5	2	no	—
116	C₄×#108	—	5	2	no	—
117	C₄×#108	—	5	2	no	—
118	C₂³×D₅	C₂×Q₈	1	1	yes	characteristic
119	C₂²×C₄×C₅	C₂×Q₈	1	1	yes	characteristic
120	C₂²×C₄×C₅	C₂×Q₈	1	1	yes	characteristic
121	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
122	C₂²×Dic₅	C₂×Q₈	1	1	yes	characteristic
123	C₂²×Dic₅	C₂×Q₈	1	1	yes	characteristic
124	C₂²×Dic₅	C₂×Q₈	1	1	yes	characteristic
125	C₂×C₄×D₅	—	2	1	no	—
126	C₂×C₄×D₅	—	2	1	no	—
127	C₂×C₄×D₅	—	2	1	no	—
128	C₂×C₄×D₅	—	2	1	no	—
129	C₂×C₄×D₅	—	2	4	no	—
130	C₂×C₄×D₅	—	4	2	no	—
131	C₂×C₄×D₅	C₄⋊C₄	1	1	yes	characteristic
132	C₂×C₄×D₅	C₄⋊C₄	1	1	yes	characteristic
133	C₂×C₄×D₅	C₄⋊C₄	1	1	yes	characteristic
134	C₂×C₄×D₅	C₄⋊C₄	1	1	yes	characteristic
135	C₂×C₄×D₅	C₄⋊C₄	1	1	yes	characteristic
136	C₂×C₄×D₅	C₄⋊C₄	1	1	yes	characteristic
137	C₂×C₄×D₅	C₄⋊C₄	1	1	yes	characteristic
138	C₂×C₄×D₅	C₄⋊C₄	1	1	yes	characteristic
139	C₂×C₄×D₅	C₂²×C₄	1	1	yes	characteristic
140	C₂×C₄×D₅	C₂²×C₄	1	1	yes	characteristic
141	C₂×C₄×D₅	C₂×D₄	1	1	yes	characteristic
142	C₂×C₄×D₅	C₂×D₄	1	1	yes	characteristic
143	C₅×M₁₆	—	2	1	no	—
144	C₅×M₁₆	—	2	1	no	—
145	C₅×M₁₆	—	2	2	no	—
146	C₅×M₁₆	—	2	2	no	—
147	C₅×M₁₆	#41	1	2	yes	—
148	C₅×M₁₆	#41	1	2	yes	—
149	C₂×C₅×C₈	—	2	1	no	—
150	C₂×C₅×C₈	—	2	1	no	—
151	C₂×C₅×C₈	—	2	2	no	—
152	C₂×C₅×C₈	—	2	2	no	—
153	C₂×C₅×C₈	—	2	2	no	—
154	C₂×C₅×C₈	C₂²×C₄	1	4	yes	—
155	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
156	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
157	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
158	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
159	C₄×Dic₅	C₄⋊C₄	1	1	yes	characteristic
160	C₄×Dic₅	C₄⋊C₄	1	1	yes	characteristic
161	C₄×Dic₅	C₄⋊C₄	1	1	yes	characteristic
162	C₄×Dic₅	C₄⋊C₄	1	1	yes	characteristic
163	C₄×Dic₅	C₄⋊C₄	1	1	yes	characteristic
164	C₄×Dic₅	C₄⋊C₄	1	1	yes	characteristic
165	C₄×Dic₅	C₄⋊C₄	1	1	yes	characteristic
166	C₄×Dic₅	C₄⋊C₄	1	1	yes	characteristic
167	C₄×Dic₅	C₂²×C₄	1	1	yes	characteristic
168	C₄×Dic₅	C₂²×C₄	1	1	yes	characteristic
169	C₄×Dic₅	C₂×D₄	1	1	yes	characteristic
170	C₄×Dic₅	C₂×D₄	1	1	yes	characteristic
171	#681	—	2	1	no	—
172	#681	—	2	1	no	—
173	#681	—	2	2	no	—
174	#681	—	2	2	no	—
175	#681	#41	1	2	yes	—
176	#681	#41	1	2	yes	—
177	C₂×#168	—	2	1	no	—
178	C₂×#168	—	2	1	no	—
179	C₂×#168	—	2	2	no	—
180	C₂×#168	—	2	2	no	—
181	C₂×#168	—	2	2	no	—
182	C₂×#168	C₂²×C₄	1	4	yes	—
183	#676	—	2	4	no	—
184	#676	—	2	4	no	—
185	C₈×D₅	—	2	4	no	—
186	C₈×D₅	—	2	4	no	—
187	C₂²×M₁₆	—	5	1	no	—
188	C₂²×M₁₆	—	5	1	no	—
189	C₂²×C₄²	—	5	1	no	—
190	#432	—	10	1	no	—
191	#432	—	10	1	no	—
192	#431	—	5	2	no	—
193	#431	—	5	2	no	—
194	#431	—	5	2	no	—
195	#431	—	5	2	no	—
196	#431	—	10	1	no	—
197	#431	—	10	1	no	—
198	C₂×#108	—	5	2	no	—
199	C₂×#108	—	5	2	no	—
200	C₂×#108	—	5	2	no	—
201	C₂×#108	C₂×D₅	1	2	yes	—
202	#423	—	5	1	no	—
203	#423	C₂×D₅	1	1	yes	characteristic
204	C₂×C₄⋊C₈	—	5	1	no	—
205	C₂×C₄⋊C₈	C₂×D₅	1	1	yes	characteristic
206	#407	—	5	2	no	—
207	C₂×C₂²⋊C₈	—	5	2	no	—
208	C₄×M₁₆	—	5	1	no	—
209	C₄×M₁₆	—	5	1	no	—
210	C₄×M₁₆	—	5	2	no	—
211	C₄×M₁₆	—	5	1	no	—
212	C₄×M₁₆	—	10	1	no	—
213	C₄×M₁₆	—	10	1	no	—
214	C₄×M₁₆	C₂×D₅	1	1	yes	characteristic
215	C₂×#97	—	10	1	no	—
216	C₂×C₄×C₈	—	5	2	no	—
217	C₂×C₄×C₈	—	10	1	no	—
218	#341	—	5	2	no	—
219	#341	—	5	2	no	—
220	#341	—	5	2	no	—
221	#341	C₂×D₅	1	2	yes	—
222	C₂³×C₅	C₂²×Q₈	1	1	yes	characteristic
223	C₂²×D₅	—	2	1	no	—
224	C₂²×D₅	—	2	1	no	—
225	C₂²×D₅	—	2	2	no	—
226	C₂²×D₅	—	4	1	no	—
227	C₂²×D₅	C₂×C₄⋊C₄	1	1	yes	characteristic
228	C₂²×D₅	C₂×C₄⋊C₄	1	1	yes	characteristic
229	C₂×C₄×C₅	—	2	2	no	—
230	C₂×C₄×C₅	—	4	1	no	—
231	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
232	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
233	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
234	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
235	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
236	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
237	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
238	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
239	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
240	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
241	C₂×Dic₅	—	2	1	no	—
242	C₂×Dic₅	—	2	1	no	—
243	C₂×Dic₅	—	2	2	no	—
244	C₂×Dic₅	—	2	2	no	—
245	C₂×Dic₅	C₂×C₄⋊C₄	1	1	yes	characteristic
246	C₂×Dic₅	C₂×C₄⋊C₄	1	1	yes	characteristic
247	C₂×Dic₅	C₂×C₄⋊C₄	1	1	yes	characteristic
248	C₂×Dic₅	C₂×C₄⋊C₄	1	1	yes	characteristic
249	C₂×Dic₅	C₂×C₄⋊C₄	1	1	yes	characteristic
250	C₂×Dic₅	C₂×C₄⋊C₄	1	1	yes	characteristic
251	C₄×D₅	—	2	2	no	—
252	C₄×D₅	—	2	1	no	—
253	C₄×D₅	—	2	1	no	—
254	C₄×D₅	—	2	1	no	—
255	C₄×D₅	—	2	1	no	—
256	C₄×D₅	—	2	1	no	—
257	C₄×D₅	—	2	1	no	—
258	C₄×D₅	—	2	1	no	—
259	C₄×D₅	—	2	1	no	—
260	C₄×D₅	—	2	2	no	—
261	C₄×D₅	—	2	2	no	—
262	C₄×D₅	—	2	2	no	—
263	C₄×D₅	—	2	2	no	—
264	C₄×D₅	—	4	1	no	—
265	C₄×D₅	—	4	1	no	—
266	C₄×D₅	#108	1	4	yes	complemented
267	C₅×C₈	—	2	4	no	—
268	C₅×C₈	—	2	2	no	—
269	C₅×C₈	—	2	2	no	—
270	C₅×C₈	—	4	2	no	—
271	#168	—	2	4	no	—
272	#168	—	2	2	no	—
273	#168	—	2	2	no	—
274	#168	—	4	2	no	—
275	C₂³×C₄	—	5	1	no	—
276	C₂³×C₄	—	5	1	no	—
277	C₂³×C₄	—	5	1	no	—
278	C₂×M₁₆	—	5	1	no	—
279	C₂×M₁₆	—	5	1	no	—
280	C₂×M₁₆	—	5	2	no	—
281	C₂×M₁₆	—	10	1	no	—
282	C₂×M₁₆	—	10	1	no	—
283	C₂×M₁₆	—	10	2	no	—
284	C₂×M₁₆	—	10	2	no	—
285	C₂×M₁₆	—	10	2	no	—
286	C₂×M₁₆	—	10	2	no	—
287	C₂×M₁₆	C₂²×D₅	1	2	yes	—
288	C₂×M₁₆	C₂²×D₅	1	1	yes	characteristic
289	C₂×M₁₆	C₂²×D₅	1	1	yes	characteristic
290	C₂²×C₈	—	5	2	no	—
291	C₂²×C₈	—	10	1	no	—
292	C₂²×C₈	—	10	1	no	—
293	C₂²×C₈	C₂²×D₅	1	2	yes	—
294	C₂×C₄²	—	5	1	no	—
295	C₂×C₄²	—	5	1	no	—
296	C₂×C₄²	—	5	1	no	—
297	C₂×C₄²	—	5	1	no	—
298	C₂×C₄²	—	5	1	no	—
299	C₂×C₄²	—	5	1	no	—
300	C₂×C₄²	—	5	1	no	—
301	C₂×C₄²	—	5	1	no	—
302	C₂×C₄²	—	5	1	no	—
303	C₂×C₄²	—	5	1	no	—
304	C₂×C₄²	—	5	1	no	—
305	C₂×C₄²	C₂²×D₅	1	1	yes	characteristic
306	#108	—	2	4	no	—
307	#108	—	10	4	no	—
308	#108	—	10	4	no	—
309	#108	—	10	4	no	—
310	C₄⋊C₈	—	2	1	no	—
311	C₄⋊C₈	—	2	1	no	—
312	C₄⋊C₈	—	5	2	no	—
313	C₄⋊C₈	—	5	2	no	—
314	C₄⋊C₈	—	10	1	no	—
315	C₄⋊C₈	—	10	1	no	—
316	C₄⋊C₈	C₄×D₅	1	2	yes	—
317	C₄⋊C₈	C₄×D₅	1	2	yes	—
318	C₂²⋊C₈	—	5	4	no	—
319	C₂²⋊C₈	—	5	4	no	—
320	C₂²⋊C₈	—	10	2	no	—
321	C₂²⋊C₈	—	10	2	no	—
322	#97	—	2	1	no	—
323	#97	—	10	1	no	—
324	#97	—	10	1	no	—
325	#97	—	10	2	no	—
326	#97	—	10	1	no	—
327	C₄×C₈	—	2	1	no	—
328	C₄×C₈	—	5	4	no	—
329	C₄×C₈	—	5	4	no	—
330	C₄×C₈	—	10	1	no	—
331	C₄×C₈	—	10	1	no	—
332	C₄×C₈	—	10	2	no	—
333	C₄×C₈	—	10	1	no	—
334	C₂²×C₅	—	2	1	no	—
335	C₂²×C₅	—	2	1	no	—
336	C₂²×C₅	C₂²×C₄⋊C₄	1	1	yes	characteristic
337	C₂²×C₅	#533	1	1	yes	characteristic
338	C₂²×C₅	#533	1	1	yes	characteristic
339	C₂×D₅	—	2	1	no	—
340	C₂×D₅	—	2	1	no	—
341	C₂×D₅	—	2	1	no	—
342	C₂×D₅	—	2	1	no	—
343	C₂×D₅	—	2	1	no	—
344	C₂×D₅	—	4	2	no	—
345	C₂×D₅	—	4	2	no	—
346	C₂×D₅	C₂×#108	1	2	yes	—
347	C₄×C₅	—	2	1	no	—
348	C₄×C₅	—	2	1	no	—
349	C₄×C₅	—	2	1	no	—
350	C₄×C₅	C₂×#108	1	2	yes	—
351	C₄×C₅	C₄×#41	1	1	yes	characteristic
352	C₄×C₅	C₄×#41	1	1	yes	characteristic
353	C₄×C₅	#525	1	1	yes	characteristic
354	C₄×C₅	#525	1	1	yes	characteristic
355	Dic₅	—	2	1	no	—
356	Dic₅	—	2	1	no	—
357	Dic₅	—	2	1	no	—
358	Dic₅	—	2	1	no	—
359	Dic₅	C₂×#108	1	2	yes	—
360	Dic₅	#430	1	2	yes	—
361	C₂⁴	—	5	1	no	—
362	C₂²×C₄	—	5	1	no	—
363	C₂²×C₄	—	5	1	no	—
364	C₂²×C₄	—	5	1	no	—
365	C₂²×C₄	—	5	1	no	—
366	C₂²×C₄	—	5	1	no	—
367	C₂²×C₄	—	5	1	no	—
368	C₂²×C₄	—	5	1	no	—
369	C₂²×C₄	—	5	1	no	—
370	C₂²×C₄	—	5	1	no	—
371	C₂²×C₄	—	5	1	no	—
372	C₂²×C₄	—	5	1	no	—
373	C₂²×C₄	—	5	1	no	—
374	C₂²×C₄	—	5	1	no	—
375	C₂²×C₄	—	5	1	no	—
376	C₂²×C₄	—	5	1	no	—
377	C₂²×C₄	—	10	4	no	—
378	C₂²×C₄	—	10	1	no	—
379	C₂²×C₄	—	10	1	no	—
380	C₂²×C₄	—	10	1	no	—
381	C₂²×C₄	—	10	1	no	—
382	C₂²×C₄	—	20	2	no	—
383	C₂²×C₄	Q₈×D₅	1	1	yes	characteristic
384	C₂²×C₄	Q₈×D₅	1	1	yes	characteristic
385	C₂²×C₄	C₂³×D₅	1	1	yes	characteristic
386	M₁₆	—	2	1	no	—
387	M₁₆	—	2	1	no	—
388	M₁₆	—	2	2	no	—
389	M₁₆	—	2	2	no	—
390	M₁₆	—	5	2	no	—
391	M₁₆	—	5	2	no	—
392	M₁₆	—	10	4	no	—
393	M₁₆	—	10	4	no	—
394	M₁₆	—	10	1	no	—
395	M₁₆	—	10	1	no	—
396	M₁₆	—	10	2	no	—
397	M₁₆	—	10	2	no	—
398	M₁₆	#711	1	2	yes	—
399	M₁₆	#713	1	2	yes	—
400	C₂×C₈	—	2	1	no	—
401	C₂×C₈	—	2	1	no	—
402	C₂×C₈	—	2	2	no	—
403	C₂×C₈	—	2	2	no	—
404	C₂×C₈	—	2	2	no	—
405	C₂×C₈	—	5	4	no	—
406	C₂×C₈	—	10	4	no	—
407	C₂×C₈	—	10	4	no	—
408	C₂×C₈	—	10	1	no	—
409	C₂×C₈	—	10	1	no	—
410	C₂×C₈	—	10	2	no	—
411	C₂×C₈	—	10	2	no	—
412	C₂×C₈	—	10	2	no	—
413	C₂×C₈	C₂×C₄×D₅	1	4	yes	—
414	C₄²	—	5	1	no	—
415	C₄²	—	5	1	no	—
416	C₄²	—	5	1	no	—
417	C₄²	—	5	1	no	—
418	C₄²	—	5	1	no	—
419	C₄²	—	5	1	no	—
420	C₄²	—	5	1	no	—
421	C₄²	—	5	1	no	—
422	C₄²	—	5	1	no	—
423	C₄²	—	5	1	no	—
424	C₄²	—	5	1	no	—
425	C₄²	—	5	1	no	—
426	C₄²	C₂×C₄×D₅	1	1	yes	characteristic
427	C₄²	C₂×C₄×D₅	1	1	yes	characteristic
428	C₄²	D₄×D₅	1	1	yes	characteristic
429	C₄²	D₄×D₅	1	1	yes	characteristic
430	C₂×C₅	—	2	1	no	—
431	C₂×C₅	—	2	1	no	—
432	C₂×C₅	#2296	1	1	yes	characteristic
433	C₂×C₅	C₂²×#108	1	1	yes	characteristic
434	C₂×C₅	C₂×#430	1	1	yes	characteristic
435	D₅	—	2	2	no	—
436	D₅	—	4	1	no	—
437	C₂³	—	5	1	no	—
438	C₂³	—	5	1	no	—
439	C₂³	—	10	2	no	—
440	C₂³	—	10	1	no	—
441	C₂³	—	10	1	no	—
442	C₂³	—	20	1	no	—
443	C₂³	C₂×Q₈×D₅	1	1	yes	characteristic
444	C₂×C₄	—	2	2	no	—
445	C₂×C₄	—	4	1	no	—
446	C₂×C₄	—	5	1	no	—
447	C₂×C₄	—	5	1	no	—
448	C₂×C₄	—	5	4	no	—
449	C₂×C₄	—	5	1	no	—
450	C₂×C₄	—	5	1	no	—
451	C₂×C₄	—	5	1	no	—
452	C₂×C₄	—	5	1	no	—
453	C₂×C₄	—	10	2	no	—
454	C₂×C₄	—	10	2	no	—
455	C₂×C₄	—	10	2	no	—
456	C₂×C₄	—	10	2	no	—
457	C₂×C₄	—	10	2	no	—
458	C₂×C₄	—	10	2	no	—
459	C₂×C₄	—	10	1	no	—
460	C₂×C₄	—	10	1	no	—
461	C₂×C₄	—	10	1	no	—
462	C₂×C₄	—	10	1	no	—
463	C₂×C₄	—	10	1	no	—
464	C₂×C₄	—	10	1	no	—
465	C₂×C₄	—	10	1	no	—
466	C₂×C₄	—	10	1	no	—
467	C₂×C₄	—	10	2	no	—
468	C₂×C₄	—	10	1	no	—
469	C₂×C₄	—	10	1	no	—
470	C₂×C₄	—	20	1	no	—
471	C₂×C₄	—	20	1	no	—
472	C₂×C₄	D₅×C₄⋊C₄	1	1	yes	characteristic
473	C₂×C₄	D₅×C₄⋊C₄	1	1	yes	characteristic
474	C₂×C₄	D₅×C₄⋊C₄	1	1	yes	characteristic
475	C₂×C₄	D₅×C₄⋊C₄	1	1	yes	characteristic
476	C₂×C₄	C₂²×C₄×D₅	1	1	yes	characteristic
477	C₂×C₄	C₂×D₄×D₅	1	1	yes	characteristic
478	C₂×C₄	C₂×#711	1	1	yes	characteristic
479	C₂×C₄	C₂×#713	1	1	yes	characteristic
480	C₂×C₄	D₅×#41	1	1	yes	characteristic
481	C₂×C₄	D₅×#41	1	1	yes	characteristic
482	C₈	—	2	4	no	—
483	C₈	—	2	2	no	—
484	C₈	—	2	2	no	—
485	C₈	—	4	2	no	—
486	C₈	—	10	4	no	—
487	C₈	—	10	2	no	—
488	C₈	—	10	2	no	—
489	C₈	—	20	2	no	—
490	C₅	#21370	1	1	yes	characteristic, complemented, Sylow
491	C₂²	—	2	1	no	—
492	C₂²	—	2	1	no	—
493	C₂²	—	5	2	no	—
494	C₂²	—	10	1	no	—
495	C₂²	—	10	1	no	—
496	C₂²	—	10	1	no	—
497	C₂²	—	10	1	no	—
498	C₂²	—	10	1	no	—
499	C₂²	—	20	2	no	—
500	C₂²	—	20	2	no	—
501	C₂²	C₂×D₅×C₄⋊C₄	1	1	yes	characteristic
502	C₂²	#66022	1	1	yes	characteristic
503	C₂²	#66062	1	1	yes	characteristic
504	C₄	—	2	1	no	—
505	C₄	—	2	1	no	—
506	C₄	—	2	1	no	—
507	C₄	—	5	2	no	—
508	C₄	—	5	2	no	—
509	C₄	—	10	1	no	—
510	C₄	—	10	1	no	—
511	C₄	—	10	1	no	—
512	C₄	—	10	1	no	—
513	C₄	D₅×#108	1	2	yes	—
514	C₄	C₄×#711	1	1	yes	characteristic
515	C₄	C₄×#713	1	1	yes	characteristic
516	C₄	#65940	1	1	yes	characteristic
517	C₄	#65961	1	1	yes	characteristic
518	C₂	—	2	1	no	—
519	C₂	—	2	1	no	—
520	C₂	—	10	2	no	—
521	C₂	—	20	1	no	—
522	C₂	#10607694	1	1	yes	characteristic
523	C₂	C₂×D₅×#108	1	1	yes	characteristic
524	C₂	D₅×#430	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₅
commutator	C₂×C₄×C₅	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₅
Fitting	C₅×#1950	C₂
socle	C₂²×C₅	C₂²×C₄⋊C₄
prime radical	C₂³×D₅	C₂×Q₈
cosocle	C₂²×C₄×C₅	C₂⁴
hypercenter	#1950	D₅
hypocenter	C₅	#21370
LCS	G ▷ C₂×C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1950

Complements

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

N	H ≅ G/N	type
4. C₅×#1950	C₂	semidirect
6. Dic₅×#108	C₂	semidirect
7. #10601313	C₂	semidirect
8. #10601267	C₂	semidirect
9. #10600668	C₂	semidirect
11. #10599709	C₂	semidirect
113. #1950	D₅	semidirect
266. C₄×D₅	#108	semidirect
490. C₅	#21370	semidirect

Maximal subgroups

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

subgroup	index
#10610769	2
C₂×#65122	2
C₄×D₅×M₁₆	2
C₅×#1950	2
#10601506	2
Dic₅×#108	2
#10601313	2
#10601267	2
#10600668	2
#10599734	2
#10599709	2
#21370	5