Subgroups — #12068331

Order 1280.

712 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	#10611062	C₂	1	1	yes	maximal, characteristic
2	D₅×#432	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄×#676	C₂	1	1	yes	maximal, characteristic
4	C₅×#1568	C₂	1	1	yes	maximal, characteristic, complemented
5	#10601587	C₂	1	1	yes	maximal, characteristic, complemented
6	#10601587	C₂	1	1	yes	maximal, characteristic, complemented
7	#10600525	C₂	1	1	yes	maximal, characteristic, complemented
8	#10599364	C₂	1	2	yes	maximal, complemented
9	#10599361	C₂	1	2	yes	maximal, complemented
10	#10599324	C₂	1	2	yes	maximal, complemented
11	#10599321	C₂	1	2	yes	maximal, complemented
12	C₂²×#676	C₄	1	1	yes	characteristic
13	C₂²×#676	C₄	1	1	yes	characteristic
14	C₂×C₄²×D₅	C₂²	1	1	yes	characteristic
15	C₅×#432	C₂²	1	1	yes	characteristic
16	C₅×#432	C₂²	1	1	yes	characteristic
17	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
18	C₂×#3947	C₄	1	1	yes	characteristic
19	C₂×#3947	C₄	1	1	yes	characteristic
20	#65215	C₂²	1	1	yes	characteristic
21	#65215	C₂²	1	1	yes	characteristic
22	C₂×C₄×#168	C₂²	1	1	yes	characteristic
23	#65126	C₂²	1	2	yes	—
24	#65124	C₂²	1	2	yes	—
25	#65122	C₂²	1	2	yes	—
26	D₅×C₄⋊C₈	C₂²	1	2	yes	—
27	#65015	—	2	1	no	—
28	D₅×C₂²⋊C₈	—	2	1	no	—
29	#65008	—	2	1	no	—
30	#65007	—	2	1	no	—
31	#64996	—	2	1	no	—
32	#64994	—	2	1	no	—
33	#64994	—	2	1	no	—
34	D₅×#97	—	2	1	no	—
35	C₄×#676	C₄	1	1	yes	characteristic
36	C₄×#676	C₄	1	1	yes	characteristic
37	C₄×#676	C₄	1	1	yes	characteristic
38	C₄×#676	C₄	1	1	yes	characteristic
39	C₄×#676	C₂²	1	1	yes	characteristic
40	C₄×#676	C₂²	1	1	yes	characteristic
41	C₄×#676	C₂²	1	1	yes	characteristic
42	C₄×#676	C₂²	1	1	yes	characteristic
43	C₅×#335	C₂²	1	2	yes	complemented
44	C₅×#334	C₂²	1	2	yes	complemented
45	#64700	C₂²	1	2	yes	complemented
46	#64700	C₂²	1	2	yes	complemented
47	#64699	C₂²	1	2	yes	complemented
48	#64699	C₂²	1	2	yes	complemented
49	#64678	C₂²	1	2	yes	complemented
50	#64677	C₂²	1	2	yes	complemented
51	#17797	—	5	1	no	maximal, Sylow
52	C₂²×C₄×D₅	C₂×C₄	1	1	yes	characteristic
53	C₂²×C₄×D₅	D₄	1	1	yes	characteristic
54	C₂²×C₄×D₅	Q₈	1	1	yes	characteristic
55	C₂²×C₅×C₈	C₂×C₄	1	1	yes	characteristic
56	C₂²×C₅×C₈	C₂×C₄	1	1	yes	characteristic
57	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
58	C₂×C₄×Dic₅	C₂×C₄	1	1	yes	characteristic
59	C₂×C₄×Dic₅	D₄	1	1	yes	characteristic
60	C₂×C₄×Dic₅	Q₈	1	1	yes	characteristic
61	C₂²×#168	C₂×C₄	1	1	yes	characteristic
62	C₂²×#168	C₂×C₄	1	1	yes	characteristic
63	C₂×#676	—	2	4	no	—
64	C₂×#676	—	2	4	no	—
65	C₂×#676	—	2	2	no	—
66	C₂×#676	C₂×C₄	1	1	yes	characteristic
67	C₂×#676	C₂×C₄	1	1	yes	characteristic
68	C₂×#676	C₂×C₄	1	1	yes	characteristic
69	C₂×#676	C₂×C₄	1	1	yes	characteristic
70	C₂×#676	C₂×C₄	1	1	yes	characteristic
71	C₂×#676	C₂×C₄	1	1	yes	characteristic
72	C₂×#676	C₂×C₄	1	1	yes	characteristic
73	C₂×#676	C₂×C₄	1	1	yes	characteristic
74	C₂×C₈×D₅	—	2	2	no	—
75	C₄²×D₅	C₂×C₄	1	1	yes	characteristic
76	C₄²×D₅	C₂×C₄	1	1	yes	characteristic
77	C₄²×D₅	D₄	1	1	yes	characteristic
78	C₄²×D₅	D₄	1	1	yes	characteristic
79	C₄²×D₅	Q₈	1	1	yes	characteristic
80	C₄²×D₅	Q₈	1	1	yes	characteristic
81	C₄²×D₅	C₂³	1	1	yes	characteristic
82	C₄²×D₅	C₂³	1	1	yes	characteristic
83	C₅×C₄⋊C₈	C₂³	1	2	yes	—
84	C₅×C₄⋊C₈	C₂³	1	2	yes	—
85	C₅×C₂²⋊C₈	—	2	1	no	—
86	C₅×C₂²⋊C₈	—	2	1	no	—
87	C₅×#97	—	2	1	no	—
88	C₅×#97	—	2	1	no	—
89	C₄×C₅×C₈	C₂×C₄	1	1	yes	characteristic
90	C₄×C₅×C₈	C₂×C₄	1	1	yes	characteristic
91	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
92	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
93	C₂²⋊#168	—	2	1	no	—
94	C₂²⋊#168	—	2	1	no	—
95	#3952	—	2	2	no	—
96	#3952	—	2	2	no	—
97	#3947	—	2	2	no	—
98	#3947	C₂×C₄	1	1	yes	characteristic
99	#3947	C₂×C₄	1	1	yes	characteristic
100	#3947	C₂×C₄	1	1	yes	characteristic
101	#3947	C₂×C₄	1	1	yes	characteristic
102	#3947	C₂×C₄	1	1	yes	characteristic
103	#3947	C₂×C₄	1	1	yes	characteristic
104	#3947	C₂×C₄	1	1	yes	characteristic
105	#3947	C₂×C₄	1	1	yes	characteristic
106	#3946	—	2	2	no	—
107	#3946	—	2	2	no	—
108	C₈×Dic₅	—	2	2	no	—
109	C₄⋊#168	C₂³	1	2	yes	—
110	C₄⋊#168	C₂³	1	2	yes	—
111	#3935	—	2	1	no	—
112	#3935	—	2	1	no	—
113	C₄×#168	C₂×C₄	1	1	yes	characteristic
114	C₄×#168	C₂×C₄	1	1	yes	characteristic
115	C₄×#168	C₂³	1	1	yes	characteristic
116	C₄×#168	C₂³	1	1	yes	characteristic
117	#2920	—	5	1	no	—
118	C₂×#432	—	5	1	no	—
119	C₂×C₄×M₁₆	—	5	1	no	—
120	#1569	—	5	2	no	—
121	#1569	—	5	2	no	—
122	#1568	—	5	1	no	—
123	#1568	—	5	1	no	—
124	#1568	—	5	1	no	—
125	#1568	D₅	1	1	yes	characteristic, complemented
126	#1565	—	5	2	no	—
127	#1565	—	5	2	no	—
128	C₂³×D₅	C₄⋊C₄	1	1	yes	characteristic
129	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
130	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
131	C₂²×C₄×C₅	C₂×Q₈	1	1	yes	characteristic
132	C₂²×Dic₅	C₄⋊C₄	1	1	yes	characteristic
133	C₂²×Dic₅	C₄⋊C₄	1	1	yes	characteristic
134	C₂²×Dic₅	C₄⋊C₄	1	1	yes	characteristic
135	C₂×C₄×D₅	—	2	2	no	—
136	C₂×C₄×D₅	—	2	2	no	—
137	C₂×C₄×D₅	—	4	2	no	—
138	C₂×C₄×D₅	—	4	2	no	—
139	C₂×C₄×D₅	C₄⋊C₄	1	1	yes	characteristic
140	C₂×C₄×D₅	C₄⋊C₄	1	1	yes	characteristic
141	C₂×C₄×D₅	C₄⋊C₄	1	1	yes	characteristic
142	C₂×C₄×D₅	C₄⋊C₄	1	1	yes	characteristic
143	C₂×C₄×D₅	C₄⋊C₄	1	1	yes	characteristic
144	C₂×C₄×D₅	C₄⋊C₄	1	1	yes	characteristic
145	C₂×C₄×D₅	C₂²×C₄	1	1	yes	characteristic
146	C₂×C₄×D₅	C₂²×C₄	1	1	yes	characteristic
147	C₂×C₄×D₅	C₂×D₄	1	1	yes	characteristic
148	C₂×C₄×D₅	C₂×D₄	1	1	yes	characteristic
149	C₂×C₄×D₅	C₂×Q₈	1	1	yes	characteristic
150	C₂×C₄×D₅	C₂×Q₈	1	1	yes	characteristic
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	—	2	2	no	—
155	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
156	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
157	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
158	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
159	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
160	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
161	C₄²×C₅	C₂×Q₈	1	1	yes	characteristic
162	C₄²×C₅	C₂⁴	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	C₄⋊C₄	1	1	yes	characteristic
168	C₄×Dic₅	C₄⋊C₄	1	1	yes	characteristic
169	C₄×Dic₅	C₂²×C₄	1	1	yes	characteristic
170	C₄×Dic₅	C₂²×C₄	1	1	yes	characteristic
171	C₄×Dic₅	C₂×D₄	1	1	yes	characteristic
172	C₄×Dic₅	C₂×D₄	1	1	yes	characteristic
173	C₄×Dic₅	C₂×Q₈	1	1	yes	characteristic
174	C₄×Dic₅	C₂×Q₈	1	1	yes	characteristic
175	C₂×#168	—	2	2	no	—
176	C₂×#168	—	2	2	no	—
177	C₂×#168	—	2	2	no	—
178	C₂×#168	—	2	2	no	—
179	C₂×#168	C₂²×C₄	1	1	yes	characteristic
180	C₂×#168	C₂²×C₄	1	1	yes	characteristic
181	C₂×#168	C₂²×C₄	1	1	yes	characteristic
182	C₂×#168	C₂²×C₄	1	1	yes	characteristic
183	#676	—	2	2	no	—
184	#676	—	2	2	no	—
185	#676	—	2	2	no	—
186	#676	—	2	2	no	—
187	#676	—	2	2	no	—
188	#676	—	2	2	no	—
189	#676	—	4	4	no	—
190	#676	M₁₆	1	4	yes	complemented
191	#676	M₁₆	1	4	yes	complemented
192	C₈×D₅	—	4	4	no	—
193	C₂²×M₁₆	—	5	1	no	—
194	C₂²×M₁₆	—	5	1	no	—
195	C₂²×C₄²	—	5	1	no	—
196	#432	—	5	1	no	—
197	#432	—	5	1	no	—
198	#432	—	5	2	no	—
199	#432	—	10	1	no	—
200	#432	—	10	1	no	—
201	#432	—	10	1	no	—
202	#432	C₂×D₅	1	1	yes	characteristic
203	#432	C₂×D₅	1	1	yes	characteristic
204	#431	—	5	2	no	—
205	#431	—	10	1	no	—
206	#423	—	5	2	no	—
207	C₂×C₄⋊C₈	—	5	2	no	—
208	#407	—	10	1	no	—
209	C₂×C₂²⋊C₈	—	10	1	no	—
210	C₄×M₁₆	—	5	1	no	—
211	C₄×M₁₆	—	5	1	no	—
212	C₄×M₁₆	—	5	1	no	—
213	C₄×M₁₆	—	5	1	no	—
214	C₄×M₁₆	—	5	1	no	—
215	C₄×M₁₆	—	5	1	no	—
216	C₄×M₁₆	—	5	1	no	—
217	C₄×M₁₆	—	5	1	no	—
218	C₄×M₁₆	—	10	1	no	—
219	C₂×#97	—	5	1	no	—
220	C₂×#97	—	5	1	no	—
221	C₂×#97	—	10	1	no	—
222	C₂×C₄×C₈	—	5	1	no	—
223	C₂×C₄×C₈	C₂×D₅	1	1	yes	characteristic
224	#335	—	5	2	no	—
225	#335	—	5	2	no	—
226	#335	—	5	2	no	—
227	#335	C₂×D₅	1	2	yes	complemented
228	#334	—	5	2	no	—
229	#334	—	5	2	no	—
230	#334	—	5	2	no	—
231	#334	C₂×D₅	1	2	yes	complemented
232	C₂³×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
233	C₂²×D₅	—	2	2	no	—
234	C₂²×D₅	—	2	2	no	—
235	C₂²×D₅	—	4	1	no	—
236	C₂²×D₅	C₂×C₄⋊C₄	1	1	yes	characteristic
237	C₂²×D₅	C₂×C₄⋊C₄	1	1	yes	characteristic
238	C₂×C₄×C₅	—	2	2	no	—
239	C₂×C₄×C₅	—	2	1	no	—
240	C₂×C₄×C₅	—	2	1	no	—
241	C₂×C₄×C₅	—	2	2	no	—
242	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
243	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
244	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
245	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
246	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
247	C₂×C₄×C₅	C₂²×Q₈	1	1	yes	characteristic
248	C₂×Dic₅	—	2	2	no	—
249	C₂×Dic₅	—	2	2	no	—
250	C₂×Dic₅	—	4	1	no	—
251	C₂×Dic₅	C₂×C₄⋊C₄	1	1	yes	characteristic
252	C₂×Dic₅	C₂×C₄⋊C₄	1	1	yes	characteristic
253	C₂×Dic₅	C₂×C₄⋊C₄	1	1	yes	characteristic
254	C₂×Dic₅	C₂×C₄⋊C₄	1	1	yes	characteristic
255	C₂×Dic₅	C₂×C₄⋊C₄	1	1	yes	characteristic
256	C₂×Dic₅	C₂×C₄⋊C₄	1	1	yes	characteristic
257	C₄×D₅	—	2	2	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	—	4	1	no	—
264	C₄×D₅	—	4	1	no	—
265	C₄×D₅	—	4	1	no	—
266	C₄×D₅	—	4	1	no	—
267	C₄×D₅	—	4	1	no	—
268	C₄×D₅	—	4	1	no	—
269	C₄×D₅	C₂×M₁₆	1	2	yes	—
270	C₄×D₅	C₂×M₁₆	1	2	yes	—
271	C₅×C₈	—	2	1	no	—
272	C₅×C₈	—	2	1	no	—
273	C₅×C₈	—	4	2	no	—
274	C₅×C₈	—	4	2	no	—
275	C₅×C₈	C₂×M₁₆	1	2	yes	—
276	C₅×C₈	C₂×M₁₆	1	2	yes	—
277	#168	—	2	1	no	—
278	#168	—	2	1	no	—
279	#168	—	4	2	no	—
280	#168	—	4	2	no	—
281	#168	C₂×M₁₆	1	2	yes	—
282	#168	C₂×M₁₆	1	2	yes	—
283	C₂³×C₄	—	5	1	no	—
284	C₂³×C₄	—	5	1	no	—
285	C₂³×C₄	—	5	1	no	—
286	C₂×M₁₆	—	5	1	no	—
287	C₂×M₁₆	—	5	1	no	—
288	C₂×M₁₆	—	5	1	no	—
289	C₂×M₁₆	—	5	1	no	—
290	C₂×M₁₆	—	5	1	no	—
291	C₂×M₁₆	—	5	1	no	—
292	C₂×M₁₆	—	5	1	no	—
293	C₂×M₁₆	—	5	1	no	—
294	C₂×M₁₆	—	10	4	no	—
295	C₂×M₁₆	—	10	4	no	—
296	C₂×M₁₆	—	10	2	no	—
297	C₂²×C₈	—	5	1	no	—
298	C₂²×C₈	—	5	1	no	—
299	C₂²×C₈	—	10	2	no	—
300	C₂²×C₈	C₄×D₅	1	1	yes	characteristic
301	C₂²×C₈	C₄×D₅	1	1	yes	characteristic
302	C₂×C₄²	—	5	1	no	—
303	C₂×C₄²	—	5	1	no	—
304	C₂×C₄²	—	5	1	no	—
305	C₂×C₄²	—	5	1	no	—
306	C₂×C₄²	—	5	1	no	—
307	C₂×C₄²	—	5	1	no	—
308	C₂×C₄²	—	5	1	no	—
309	C₂×C₄²	—	5	1	no	—
310	C₂×C₄²	—	5	1	no	—
311	C₂×C₄²	—	5	1	no	—
312	C₂×C₄²	—	5	1	no	—
313	C₂×C₄²	C₂²×D₅	1	1	yes	characteristic
314	C₄⋊C₈	—	5	2	no	—
315	C₄⋊C₈	—	5	2	no	—
316	C₄⋊C₈	—	10	2	no	—
317	C₄⋊C₈	—	10	2	no	—
318	C₄⋊C₈	C₂²×D₅	1	2	yes	—
319	C₄⋊C₈	C₂²×D₅	1	2	yes	—
320	C₂²⋊C₈	—	2	1	no	—
321	C₂²⋊C₈	—	2	1	no	—
322	C₂²⋊C₈	—	10	2	no	—
323	C₂²⋊C₈	—	10	2	no	—
324	C₂²⋊C₈	—	10	1	no	—
325	C₂²⋊C₈	—	10	1	no	—
326	#97	—	2	1	no	—
327	#97	—	2	1	no	—
328	#97	—	5	1	no	—
329	#97	—	5	1	no	—
330	#97	—	5	1	no	—
331	#97	—	5	1	no	—
332	#97	—	5	1	no	—
333	#97	—	5	1	no	—
334	#97	—	5	1	no	—
335	#97	—	5	1	no	—
336	#97	—	10	2	no	—
337	#97	—	10	1	no	—
338	#97	—	10	1	no	—
339	C₄×C₈	—	5	1	no	—
340	C₄×C₈	—	5	1	no	—
341	C₄×C₈	—	5	1	no	—
342	C₄×C₈	—	5	1	no	—
343	C₄×C₈	—	10	2	no	—
344	C₄×C₈	C₄×D₅	1	1	yes	characteristic
345	C₄×C₈	C₄×D₅	1	1	yes	characteristic
346	C₄×C₈	C₂²×D₅	1	1	yes	characteristic
347	C₄×C₈	C₂²×D₅	1	1	yes	characteristic
348	C₂²×C₅	—	2	1	no	—
349	C₂²×C₅	—	2	1	no	—
350	C₂²×C₅	#430	1	2	yes	—
351	C₂²×C₅	C₂²×C₄⋊C₄	1	1	yes	characteristic
352	C₂×D₅	—	2	1	no	—
353	C₂×D₅	—	2	1	no	—
354	C₂×D₅	—	2	1	no	—
355	C₂×D₅	—	2	1	no	—
356	C₂×D₅	—	2	1	no	—
357	C₂×D₅	—	4	4	no	—
358	C₂×D₅	#423	1	2	yes	—
359	C₄×C₅	—	2	1	no	—
360	C₄×C₅	—	2	1	no	—
361	C₄×C₅	—	2	1	no	—
362	C₄×C₅	—	2	1	no	—
363	C₄×C₅	C₂²×M₁₆	1	1	yes	characteristic
364	C₄×C₅	C₂²×M₁₆	1	1	yes	characteristic
365	C₄×C₅	#575	1	2	yes	—
366	Dic₅	—	2	1	no	—
367	Dic₅	—	2	1	no	—
368	Dic₅	—	2	1	no	—
369	Dic₅	—	2	1	no	—
370	Dic₅	—	2	1	no	—
371	Dic₅	#423	1	2	yes	—
372	C₂⁴	—	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	—	5	1	no	—
378	C₂²×C₄	—	5	1	no	—
379	C₂²×C₄	—	5	1	no	—
380	C₂²×C₄	—	5	1	no	—
381	C₂²×C₄	—	5	1	no	—
382	C₂²×C₄	—	5	1	no	—
383	C₂²×C₄	—	5	1	no	—
384	C₂²×C₄	—	5	1	no	—
385	C₂²×C₄	—	5	1	no	—
386	C₂²×C₄	—	5	1	no	—
387	C₂²×C₄	—	5	1	no	—
388	C₂²×C₄	—	10	2	no	—
389	C₂²×C₄	—	10	2	no	—
390	C₂²×C₄	—	20	2	no	—
391	C₂²×C₄	—	20	2	no	—
392	C₂²×C₄	C₂×C₄×D₅	1	1	yes	characteristic
393	C₂²×C₄	D₄×D₅	1	1	yes	characteristic
394	C₂²×C₄	Q₈×D₅	1	1	yes	characteristic
395	M₁₆	—	5	4	no	—
396	M₁₆	—	5	4	no	—
397	M₁₆	—	10	2	no	—
398	M₁₆	—	10	2	no	—
399	M₁₆	—	10	2	no	—
400	M₁₆	—	10	2	no	—
401	M₁₆	—	10	2	no	—
402	M₁₆	—	10	2	no	—
403	M₁₆	—	20	4	no	—
404	C₂×C₈	—	2	2	no	—
405	C₂×C₈	—	2	2	no	—
406	C₂×C₈	—	2	2	no	—
407	C₂×C₈	—	2	2	no	—
408	C₂×C₈	—	5	1	no	—
409	C₂×C₈	—	5	1	no	—
410	C₂×C₈	—	5	1	no	—
411	C₂×C₈	—	5	1	no	—
412	C₂×C₈	—	10	2	no	—
413	C₂×C₈	—	10	2	no	—
414	C₂×C₈	—	10	2	no	—
415	C₂×C₈	—	10	2	no	—
416	C₂×C₈	—	20	4	no	—
417	C₂×C₈	C₂×C₄×D₅	1	1	yes	characteristic
418	C₂×C₈	C₂×C₄×D₅	1	1	yes	characteristic
419	C₂×C₈	C₂×C₄×D₅	1	1	yes	characteristic
420	C₂×C₈	C₂×C₄×D₅	1	1	yes	characteristic
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	—	5	1	no	—
427	C₄²	—	5	1	no	—
428	C₄²	—	5	1	no	—
429	C₄²	—	5	1	no	—
430	C₄²	—	5	1	no	—
431	C₄²	—	5	1	no	—
432	C₄²	—	5	1	no	—
433	C₄²	C₂×C₄×D₅	1	1	yes	characteristic
434	C₄²	D₄×D₅	1	1	yes	characteristic
435	C₄²	Q₈×D₅	1	1	yes	characteristic
436	C₄²	C₂³×D₅	1	1	yes	characteristic
437	C₂×C₅	—	2	2	no	—
438	C₂×C₅	C₂×#423	1	1	yes	characteristic
439	C₂×C₅	#2911	1	1	yes	characteristic
440	C₂×C₅	C₂×#430	1	1	yes	characteristic
441	D₅	—	2	2	no	—
442	D₅	—	4	1	no	—
443	C₂³	—	5	1	no	—
444	C₂³	—	5	1	no	—
445	C₂³	—	10	2	no	—
446	C₂³	—	10	2	no	—
447	C₂³	—	20	1	no	—
448	C₂³	D₅×C₄⋊C₄	1	1	yes	characteristic
449	C₂×C₄	—	2	2	no	—
450	C₂×C₄	—	2	1	no	—
451	C₂×C₄	—	2	1	no	—
452	C₂×C₄	—	2	2	no	—
453	C₂×C₄	—	5	1	no	—
454	C₂×C₄	—	5	2	no	—
455	C₂×C₄	—	5	2	no	—
456	C₂×C₄	—	5	1	no	—
457	C₂×C₄	—	5	1	no	—
458	C₂×C₄	—	5	1	no	—
459	C₂×C₄	—	5	1	no	—
460	C₂×C₄	—	5	1	no	—
461	C₂×C₄	—	10	2	no	—
462	C₂×C₄	—	10	2	no	—
463	C₂×C₄	—	10	2	no	—
464	C₂×C₄	—	10	2	no	—
465	C₂×C₄	—	10	1	no	—
466	C₂×C₄	—	10	1	no	—
467	C₂×C₄	—	10	2	no	—
468	C₂×C₄	—	10	2	no	—
469	C₂×C₄	—	20	1	no	—
470	C₂×C₄	—	20	1	no	—
471	C₂×C₄	—	20	1	no	—
472	C₂×C₄	—	20	1	no	—
473	C₂×C₄	—	20	1	no	—
474	C₂×C₄	—	20	1	no	—
475	C₂×C₄	—	20	1	no	—
476	C₂×C₄	D₅×C₄⋊C₄	1	1	yes	characteristic
477	C₂×C₄	D₅×C₄⋊C₄	1	1	yes	characteristic
478	C₂×C₄	D₅×C₄⋊C₄	1	1	yes	characteristic
479	C₂×C₄	C₂²×C₄×D₅	1	1	yes	characteristic
480	C₂×C₄	C₂×D₄×D₅	1	1	yes	characteristic
481	C₂×C₄	C₂×Q₈×D₅	1	1	yes	characteristic
482	C₈	—	2	1	no	—
483	C₈	—	2	1	no	—
484	C₈	—	4	2	no	—
485	C₈	—	4	2	no	—
486	C₈	—	5	2	no	—
487	C₈	—	5	2	no	—
488	C₈	—	10	1	no	—
489	C₈	—	10	1	no	—
490	C₈	—	20	2	no	—
491	C₈	—	20	2	no	—
492	C₈	D₅×M₁₆	1	2	yes	—
493	C₈	D₅×M₁₆	1	2	yes	—
494	C₅	#17797	1	1	yes	characteristic, complemented, Sylow
495	C₂²	—	2	1	no	—
496	C₂²	—	2	1	no	—
497	C₂²	—	5	2	no	—
498	C₂²	—	10	1	no	—
499	C₂²	—	10	1	no	—
500	C₂²	—	10	1	no	—
501	C₂²	—	10	1	no	—
502	C₂²	—	10	1	no	—
503	C₂²	—	20	4	no	—
504	C₂²	#65182	1	2	yes	—
505	C₂²	C₂×D₅×C₄⋊C₄	1	1	yes	characteristic
506	C₄	—	2	1	no	—
507	C₄	—	2	1	no	—
508	C₄	—	2	1	no	—
509	C₄	—	2	1	no	—
510	C₄	—	5	2	no	—
511	C₄	—	10	1	no	—
512	C₄	—	10	1	no	—
513	C₄	—	10	1	no	—
514	C₄	—	10	1	no	—
515	C₄	—	10	1	no	—
516	C₄	C₂×D₅×M₁₆	1	1	yes	characteristic
517	C₄	C₂×D₅×M₁₆	1	1	yes	characteristic
518	C₄	#66102	1	2	yes	—
519	C₂	—	2	2	no	—
520	C₂	—	10	2	no	—
521	C₂	—	20	1	no	—
522	C₂	D₅×#423	1	1	yes	characteristic
523	C₂	#10610908	1	1	yes	characteristic
524	C₂	C₂×#65182	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₅
commutator	C₂×C₄×C₅	C₂³×C₄
Frattini	C₄²	C₂³×D₅
Fitting	C₅×#1568	C₂
socle	C₂²×C₅	C₂²×C₄⋊C₄
prime radical	C₂³×D₅	C₄⋊C₄
cosocle	C₄²×C₅	C₂⁴
hypercenter	#1568	D₅
hypocenter	C₅	#17797
LCS	G ▷ C₂×C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1568

Complements

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

N	H ≅ G/N	type
4. C₅×#1568	C₂	semidirect
5. #10601587	C₂	semidirect
6. #10601587	C₂	semidirect
7. #10600525	C₂	semidirect
8. #10599364	C₂	semidirect
9. #10599361	C₂	semidirect
10. #10599324	C₂	semidirect
11. #10599321	C₂	semidirect
43. C₅×#335	C₂²	semidirect
44. C₅×#334	C₂²	semidirect
45. #64700	C₂²	semidirect
46. #64700	C₂²	semidirect
47. #64699	C₂²	semidirect
48. #64699	C₂²	semidirect
49. #64678	C₂²	semidirect
50. #64677	C₂²	semidirect
125. #1568	D₅	semidirect
190. #676	M₁₆	semidirect
191. #676	M₁₆	semidirect
227. #335	C₂×D₅	semidirect
231. #334	C₂×D₅	semidirect
494. C₅	#17797	semidirect

Maximal subgroups

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

subgroup	index
#10611062	2
D₅×#432	2
C₂×C₄×#676	2
C₅×#1568	2
#10601587	2
#10600525	2
#10599364	2
#10599361	2
#10599324	2
#10599321	2
#17797	5