Subgroups — #12068332

Order 1280.

712 conjugacy classes of subgroups.

The subgroup lattice has 508 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#10611013	C₂	1	1	yes	maximal, characteristic
2	C₂×#65124	C₂	1	1	yes	maximal, characteristic
3	C₄×D₅×M₁₆	C₂	1	1	yes	maximal, characteristic
4	C₅×#1565	C₂	1	1	yes	maximal, characteristic, complemented
5	#10601539	C₂	1	1	yes	maximal, characteristic, complemented
6	#10601213	C₂	1	1	yes	maximal, characteristic, complemented
7	#10600643	C₂	1	1	yes	maximal, characteristic, complemented
8	#10599364	C₂	1	2	yes	maximal, complemented
9	#10599363	C₂	1	2	yes	maximal, complemented
10	#10599324	C₂	1	2	yes	maximal, complemented
11	#10599323	C₂	1	2	yes	maximal, complemented
12	C₂×D₅×M₁₆	C₄	1	1	yes	characteristic
13	C₂×D₅×M₁₆	C₄	1	1	yes	characteristic
14	C₂×C₄²×D₅	C₂²	1	1	yes	characteristic
15	C₅×#431	C₂²	1	1	yes	characteristic
16	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
17	C₄×C₅×M₁₆	C₂²	1	1	yes	characteristic
18	M₁₆×Dic₅	C₄	1	1	yes	characteristic
19	M₁₆×Dic₅	C₄	1	1	yes	characteristic
20	C₂×#3952	—	2	1	no	—
21	C₂×#3947	—	2	1	no	—
22	#65214	C₂²	1	1	yes	characteristic
23	C₂×C₄⋊#168	C₂²	1	1	yes	characteristic
24	C₄×#681	C₂²	1	1	yes	characteristic
25	#65126	C₂²	1	1	yes	characteristic
26	#65126	C₂²	1	1	yes	characteristic
27	#65124	—	2	1	no	—
28	#65124	—	2	1	no	—
29	#65124	C₂²	1	2	yes	—
30	#65124	C₂²	1	2	yes	—
31	#65124	C₂²	1	1	yes	characteristic
32	#65124	C₂²	1	1	yes	characteristic
33	#65015	—	2	1	no	—
34	#65008	—	2	1	no	—
35	#64996	C₄	1	2	yes	—
36	D₅×#97	C₄	1	2	yes	—
37	C₄×#676	—	2	1	no	—
38	C₄×#676	C₂²	1	2	yes	—
39	#64974	—	2	1	no	—
40	C₄×C₈×D₅	C₂²	1	2	yes	—
41	C₅×#335	C₂²	1	2	yes	complemented
42	C₅×#334	C₂²	1	2	yes	complemented
43	#64700	C₂²	1	2	yes	complemented
44	#64700	C₂²	1	2	yes	complemented
45	#64699	C₂²	1	2	yes	complemented
46	#64699	C₂²	1	2	yes	complemented
47	#64678	C₂²	1	2	yes	complemented
48	#64677	C₂²	1	2	yes	complemented
49	#17797	—	5	1	no	maximal, Sylow
50	C₂²×C₄×D₅	C₂×C₄	1	1	yes	characteristic
51	C₂²×C₄×D₅	D₄	1	1	yes	characteristic
52	C₂²×C₄×D₅	Q₈	1	1	yes	characteristic
53	C₂×C₅×M₁₆	C₂×C₄	1	1	yes	characteristic
54	C₂×C₅×M₁₆	C₂×C₄	1	1	yes	characteristic
55	C₂²×C₅×C₈	—	2	1	no	—
56	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
57	C₂×C₄×Dic₅	C₂×C₄	1	1	yes	characteristic
58	C₂×C₄×Dic₅	D₄	1	1	yes	characteristic
59	C₂×C₄×Dic₅	Q₈	1	1	yes	characteristic
60	C₂×#681	C₂×C₄	1	1	yes	characteristic
61	C₂×#681	C₂×C₄	1	1	yes	characteristic
62	C₂²×#168	—	2	1	no	—
63	D₅×M₁₆	—	2	4	no	—
64	D₅×M₁₆	—	2	4	no	—
65	C₂×#676	—	2	1	no	—
66	C₂×#676	—	2	1	no	—
67	C₂×#676	C₂×C₄	1	2	yes	—
68	C₂×#676	C₂×C₄	1	2	yes	—
69	C₂×C₈×D₅	C₂×C₄	1	2	yes	—
70	C₂×C₈×D₅	C₂×C₄	1	2	yes	—
71	C₄²×D₅	C₂×C₄	1	1	yes	characteristic
72	C₄²×D₅	C₂×C₄	1	1	yes	characteristic
73	C₄²×D₅	D₄	1	1	yes	characteristic
74	C₄²×D₅	D₄	1	1	yes	characteristic
75	C₄²×D₅	Q₈	1	1	yes	characteristic
76	C₄²×D₅	Q₈	1	1	yes	characteristic
77	C₄²×D₅	C₂³	1	1	yes	characteristic
78	C₄²×D₅	C₂³	1	1	yes	characteristic
79	C₅×C₄⋊C₈	—	2	1	no	—
80	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
81	C₅×C₄⋊C₈	C₂³	1	2	yes	—
82	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
83	C₅×C₂²⋊C₈	—	2	1	no	—
84	C₅×#97	C₂×C₄	1	2	yes	—
85	C₄×C₅×C₈	—	2	1	no	—
86	C₄×C₅×C₈	C₂³	1	2	yes	—
87	C₂²⋊#168	—	2	1	no	—
88	#3952	—	2	2	no	—
89	#3952	—	2	2	no	—
90	#3952	—	2	1	no	—
91	#3952	—	2	1	no	—
92	#3947	—	2	2	no	—
93	#3947	—	2	2	no	—
94	#3947	—	2	1	no	—
95	#3947	—	2	1	no	—
96	#3947	C₂×C₄	1	2	yes	—
97	#3947	C₂×C₄	1	2	yes	—
98	#3946	—	2	1	no	—
99	#3946	—	2	1	no	—
100	C₈×Dic₅	C₂×C₄	1	2	yes	—
101	C₈×Dic₅	C₂×C₄	1	2	yes	—
102	C₄⋊#168	—	2	1	no	—
103	C₄⋊#168	C₂³	1	2	yes	—
104	C₄⋊#168	C₂³	1	1	yes	characteristic
105	C₄⋊#168	C₂³	1	1	yes	characteristic
106	#3935	C₂×C₄	1	2	yes	—
107	C₄×#168	—	2	1	no	—
108	C₄×#168	C₂³	1	2	yes	—
109	#2920	—	5	1	no	—
110	C₂×#432	—	5	1	no	—
111	C₂×C₄×M₁₆	—	5	1	no	—
112	#1569	—	5	2	no	—
113	#1569	—	5	2	no	—
114	#1568	—	5	2	no	—
115	#1568	—	5	2	no	—
116	#1565	—	5	1	no	—
117	#1565	—	5	1	no	—
118	#1565	—	5	1	no	—
119	#1565	D₅	1	1	yes	characteristic, complemented
120	C₂³×D₅	C₄⋊C₄	1	1	yes	characteristic
121	C₂²×C₄×C₅	C₂²×C₄	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×Dic₅	C₄⋊C₄	1	1	yes	characteristic
125	C₂²×Dic₅	C₄⋊C₄	1	1	yes	characteristic
126	C₂²×Dic₅	C₄⋊C₄	1	1	yes	characteristic
127	C₂×C₄×D₅	—	2	2	no	—
128	C₂×C₄×D₅	—	2	2	no	—
129	C₂×C₄×D₅	—	4	1	no	—
130	C₂×C₄×D₅	—	4	1	no	—
131	C₂×C₄×D₅	—	4	2	no	—
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	C₂²×C₄	1	1	yes	characteristic
139	C₂×C₄×D₅	C₂²×C₄	1	1	yes	characteristic
140	C₂×C₄×D₅	C₂×D₄	1	1	yes	characteristic
141	C₂×C₄×D₅	C₂×D₄	1	1	yes	characteristic
142	C₂×C₄×D₅	C₂×Q₈	1	1	yes	characteristic
143	C₂×C₄×D₅	C₂×Q₈	1	1	yes	characteristic
144	C₅×M₁₆	—	2	2	no	—
145	C₅×M₁₆	M₁₆	1	4	yes	complemented
146	C₂×C₅×C₈	—	2	2	no	—
147	C₂×C₅×C₈	—	2	1	no	—
148	C₂×C₅×C₈	—	2	1	no	—
149	C₂×C₅×C₈	—	4	2	no	—
150	C₂×C₅×C₈	C₂²×C₄	1	2	yes	—
151	C₂×C₅×C₈	C₂²×C₄	1	2	yes	—
152	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
153	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
154	C₄²×C₅	C₂×Q₈	1	1	yes	characteristic
155	C₄²×C₅	C₂⁴	1	1	yes	characteristic
156	C₄×Dic₅	C₄⋊C₄	1	1	yes	characteristic
157	C₄×Dic₅	C₄⋊C₄	1	1	yes	characteristic
158	C₄×Dic₅	C₄⋊C₄	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	C₂²×C₄	1	1	yes	characteristic
163	C₄×Dic₅	C₂²×C₄	1	1	yes	characteristic
164	C₄×Dic₅	C₂×D₄	1	1	yes	characteristic
165	C₄×Dic₅	C₂×D₄	1	1	yes	characteristic
166	C₄×Dic₅	C₂×Q₈	1	1	yes	characteristic
167	C₄×Dic₅	C₂×Q₈	1	1	yes	characteristic
168	#681	—	2	2	no	—
169	#681	M₁₆	1	4	yes	complemented
170	C₂×#168	—	2	1	no	—
171	C₂×#168	—	2	1	no	—
172	C₂×#168	—	2	2	no	—
173	C₂×#168	—	4	2	no	—
174	C₂×#168	C₂²×C₄	1	2	yes	—
175	C₂×#168	C₂²×C₄	1	2	yes	—
176	#676	—	2	4	no	—
177	#676	—	2	4	no	—
178	#676	—	4	2	no	—
179	#676	—	4	2	no	—
180	C₈×D₅	—	2	4	no	—
181	C₈×D₅	—	2	4	no	—
182	C₂²×M₁₆	—	5	1	no	—
183	C₂²×M₁₆	—	5	1	no	—
184	C₂²×C₄²	—	5	1	no	—
185	#432	—	5	2	no	—
186	#432	—	5	1	no	—
187	#432	—	5	1	no	—
188	#432	—	5	2	no	—
189	#432	—	10	1	no	—
190	#432	—	10	1	no	—
191	#432	—	10	1	no	—
192	#431	—	5	1	no	—
193	#431	—	10	1	no	—
194	#431	C₂×D₅	1	1	yes	characteristic
195	#423	—	5	1	no	—
196	#423	—	5	1	no	—
197	C₂×C₄⋊C₈	—	5	1	no	—
198	C₂×C₄⋊C₈	C₂×D₅	1	1	yes	characteristic
199	#407	—	10	1	no	—
200	C₂×C₂²⋊C₈	—	10	1	no	—
201	C₄×M₁₆	—	5	1	no	—
202	C₄×M₁₆	—	5	1	no	—
203	C₄×M₁₆	—	5	1	no	—
204	C₄×M₁₆	—	5	2	no	—
205	C₄×M₁₆	—	5	2	no	—
206	C₄×M₁₆	—	10	1	no	—
207	C₄×M₁₆	C₂×D₅	1	1	yes	characteristic
208	C₂×#97	—	5	2	no	—
209	C₂×#97	—	10	1	no	—
210	C₂×C₄×C₈	—	5	2	no	—
211	#335	—	5	2	no	—
212	#335	—	5	2	no	—
213	#335	—	5	2	no	—
214	#335	C₂×D₅	1	2	yes	complemented
215	#334	—	5	2	no	—
216	#334	—	5	2	no	—
217	#334	—	5	2	no	—
218	#334	C₂×D₅	1	2	yes	complemented
219	C₂³×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
220	C₂²×D₅	—	2	2	no	—
221	C₂²×D₅	—	2	2	no	—
222	C₂²×D₅	—	4	1	no	—
223	C₂²×D₅	C₂×C₄⋊C₄	1	1	yes	characteristic
224	C₂²×D₅	C₂×C₄⋊C₄	1	1	yes	characteristic
225	C₂×C₄×C₅	—	2	1	no	—
226	C₂×C₄×C₅	—	2	1	no	—
227	C₂×C₄×C₅	—	4	1	no	—
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	C₂×C₄⋊C₄	1	1	yes	characteristic
231	C₂×C₄×C₅	C₂×M₁₆	1	2	yes	—
232	C₂×C₄×C₅	C₂×M₁₆	1	2	yes	—
233	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
234	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
235	C₂×C₄×C₅	C₂²×Q₈	1	1	yes	characteristic
236	C₂×Dic₅	—	2	2	no	—
237	C₂×Dic₅	—	4	1	no	—
238	C₂×Dic₅	—	4	1	no	—
239	C₂×Dic₅	C₂×C₄⋊C₄	1	1	yes	characteristic
240	C₂×Dic₅	C₂×C₄⋊C₄	1	1	yes	characteristic
241	C₂×Dic₅	C₂×C₄⋊C₄	1	1	yes	characteristic
242	C₂×Dic₅	C₂×C₄⋊C₄	1	1	yes	characteristic
243	C₂×Dic₅	C₂×C₄⋊C₄	1	1	yes	characteristic
244	C₂×Dic₅	C₂×C₄⋊C₄	1	1	yes	characteristic
245	C₄×D₅	—	2	2	no	—
246	C₄×D₅	—	2	2	no	—
247	C₄×D₅	—	2	1	no	—
248	C₄×D₅	—	2	1	no	—
249	C₄×D₅	—	2	1	no	—
250	C₄×D₅	—	2	1	no	—
251	C₄×D₅	—	2	1	no	—
252	C₄×D₅	—	2	1	no	—
253	C₄×D₅	—	2	1	no	—
254	C₄×D₅	—	2	1	no	—
255	C₄×D₅	—	2	2	no	—
256	C₄×D₅	—	2	2	no	—
257	C₄×D₅	—	4	1	no	—
258	C₄×D₅	—	4	1	no	—
259	C₄×D₅	—	4	1	no	—
260	C₄×D₅	—	4	1	no	—
261	C₅×C₈	—	2	2	no	—
262	C₅×C₈	—	4	1	no	—
263	C₅×C₈	—	4	1	no	—
264	C₅×C₈	—	4	2	no	—
265	C₅×C₈	C₂×M₁₆	1	4	yes	—
266	#168	—	2	2	no	—
267	#168	—	4	1	no	—
268	#168	—	4	1	no	—
269	#168	—	4	2	no	—
270	#168	C₂×M₁₆	1	4	yes	—
271	C₂³×C₄	—	5	1	no	—
272	C₂³×C₄	—	5	1	no	—
273	C₂³×C₄	—	5	1	no	—
274	C₂×M₁₆	—	5	1	no	—
275	C₂×M₁₆	—	5	1	no	—
276	C₂×M₁₆	—	5	2	no	—
277	C₂×M₁₆	—	5	2	no	—
278	C₂×M₁₆	—	10	1	no	—
279	C₂×M₁₆	—	10	1	no	—
280	C₂×M₁₆	—	10	4	no	—
281	C₂×M₁₆	—	10	4	no	—
282	C₂×M₁₆	C₄×D₅	1	1	yes	characteristic
283	C₂×M₁₆	C₄×D₅	1	1	yes	characteristic
284	C₂²×C₈	—	2	1	no	—
285	C₂²×C₈	—	5	2	no	—
286	C₂²×C₈	—	5	2	no	—
287	C₂²×C₈	—	10	1	no	—
288	C₂×C₄²	—	5	1	no	—
289	C₂×C₄²	—	5	1	no	—
290	C₂×C₄²	—	5	1	no	—
291	C₂×C₄²	—	5	1	no	—
292	C₂×C₄²	—	5	1	no	—
293	C₂×C₄²	—	5	1	no	—
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	C₂²×D₅	1	1	yes	characteristic
300	C₄⋊C₈	—	2	1	no	—
301	C₄⋊C₈	—	5	2	no	—
302	C₄⋊C₈	—	5	1	no	—
303	C₄⋊C₈	—	5	1	no	—
304	C₄⋊C₈	—	10	1	no	—
305	C₄⋊C₈	—	10	1	no	—
306	C₄⋊C₈	—	10	1	no	—
307	C₄⋊C₈	C₂²×D₅	1	1	yes	characteristic
308	C₄⋊C₈	C₂²×D₅	1	2	yes	—
309	C₄⋊C₈	C₂²×D₅	1	1	yes	characteristic
310	C₂²⋊C₈	—	2	1	no	—
311	C₂²⋊C₈	—	10	2	no	—
312	C₂²⋊C₈	—	10	2	no	—
313	C₂²⋊C₈	—	10	1	no	—
314	C₂²⋊C₈	—	10	1	no	—
315	C₂²⋊C₈	—	10	1	no	—
316	#97	—	5	2	no	—
317	#97	—	5	2	no	—
318	#97	—	5	2	no	—
319	#97	—	10	2	no	—
320	#97	—	10	2	no	—
321	#97	—	10	1	no	—
322	#97	—	10	1	no	—
323	#97	C₄×D₅	1	2	yes	—
324	C₄×C₈	—	2	1	no	—
325	C₄×C₈	—	5	2	no	—
326	C₄×C₈	—	5	2	no	—
327	C₄×C₈	—	5	2	no	—
328	C₄×C₈	—	10	1	no	—
329	C₄×C₈	C₂²×D₅	1	2	yes	—
330	C₂²×C₅	—	2	1	no	—
331	C₂²×C₅	—	2	1	no	—
332	C₂²×C₅	#423	1	2	yes	—
333	C₂²×C₅	C₂²×C₄⋊C₄	1	1	yes	characteristic
334	C₂×D₅	—	2	1	no	—
335	C₂×D₅	—	2	1	no	—
336	C₂×D₅	—	2	1	no	—
337	C₂×D₅	—	2	1	no	—
338	C₂×D₅	—	2	1	no	—
339	C₂×D₅	—	4	4	no	—
340	C₂×D₅	#430	1	2	yes	—
341	C₄×C₅	—	2	1	no	—
342	C₄×C₅	—	2	1	no	—
343	C₄×C₅	—	2	1	no	—
344	C₄×C₅	#423	1	2	yes	—
345	C₄×C₅	C₂²×M₁₆	1	1	yes	characteristic
346	C₄×C₅	C₂²×M₁₆	1	1	yes	characteristic
347	C₄×C₅	#575	1	1	yes	characteristic
348	C₄×C₅	#575	1	1	yes	characteristic
349	Dic₅	—	2	1	no	—
350	Dic₅	—	2	1	no	—
351	Dic₅	—	2	1	no	—
352	Dic₅	—	2	1	no	—
353	Dic₅	—	2	1	no	—
354	Dic₅	—	2	1	no	—
355	C₂⁴	—	5	1	no	—
356	C₂²×C₄	—	5	1	no	—
357	C₂²×C₄	—	5	1	no	—
358	C₂²×C₄	—	5	1	no	—
359	C₂²×C₄	—	5	1	no	—
360	C₂²×C₄	—	5	1	no	—
361	C₂²×C₄	—	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	—	10	2	no	—
372	C₂²×C₄	—	10	2	no	—
373	C₂²×C₄	—	20	1	no	—
374	C₂²×C₄	—	20	1	no	—
375	C₂²×C₄	—	20	2	no	—
376	C₂²×C₄	C₂×C₄×D₅	1	1	yes	characteristic
377	C₂²×C₄	D₄×D₅	1	1	yes	characteristic
378	C₂²×C₄	Q₈×D₅	1	1	yes	characteristic
379	M₁₆	—	2	2	no	—
380	M₁₆	—	5	4	no	—
381	M₁₆	—	10	4	no	—
382	M₁₆	—	10	2	no	—
383	M₁₆	—	10	4	no	—
384	M₁₆	—	20	2	no	—
385	M₁₆	—	20	2	no	—
386	M₁₆	#676	1	4	yes	complemented
387	C₂×C₈	—	2	1	no	—
388	C₂×C₈	—	2	1	no	—
389	C₂×C₈	—	2	2	no	—
390	C₂×C₈	—	4	2	no	—
391	C₂×C₈	—	5	2	no	—
392	C₂×C₈	—	5	2	no	—
393	C₂×C₈	—	10	4	no	—
394	C₂×C₈	—	10	4	no	—
395	C₂×C₈	—	10	1	no	—
396	C₂×C₈	—	10	1	no	—
397	C₂×C₈	—	10	2	no	—
398	C₂×C₈	—	20	2	no	—
399	C₂×C₈	C₂×C₄×D₅	1	2	yes	—
400	C₂×C₈	C₂×C₄×D₅	1	2	yes	—
401	C₄²	—	5	1	no	—
402	C₄²	—	5	1	no	—
403	C₄²	—	5	1	no	—
404	C₄²	—	5	1	no	—
405	C₄²	—	5	1	no	—
406	C₄²	—	5	1	no	—
407	C₄²	—	5	1	no	—
408	C₄²	—	5	1	no	—
409	C₄²	—	5	1	no	—
410	C₄²	—	5	1	no	—
411	C₄²	—	5	1	no	—
412	C₄²	—	5	1	no	—
413	C₄²	C₂×C₄×D₅	1	1	yes	characteristic
414	C₄²	D₄×D₅	1	1	yes	characteristic
415	C₄²	Q₈×D₅	1	1	yes	characteristic
416	C₄²	C₂³×D₅	1	1	yes	characteristic
417	C₂×C₅	—	2	2	no	—
418	C₂×C₅	C₂×#423	1	1	yes	characteristic
419	C₂×C₅	#2911	1	1	yes	characteristic
420	C₂×C₅	C₂×#430	1	1	yes	characteristic
421	D₅	—	2	2	no	—
422	D₅	—	4	1	no	—
423	C₂³	—	5	1	no	—
424	C₂³	—	5	1	no	—
425	C₂³	—	10	2	no	—
426	C₂³	—	10	2	no	—
427	C₂³	—	20	1	no	—
428	C₂³	D₅×C₄⋊C₄	1	1	yes	characteristic
429	C₂×C₄	—	2	1	no	—
430	C₂×C₄	—	2	1	no	—
431	C₂×C₄	—	4	1	no	—
432	C₂×C₄	—	5	1	no	—
433	C₂×C₄	—	5	1	no	—
434	C₂×C₄	—	5	1	no	—
435	C₂×C₄	—	5	1	no	—
436	C₂×C₄	—	5	1	no	—
437	C₂×C₄	—	5	1	no	—
438	C₂×C₄	—	10	2	no	—
439	C₂×C₄	—	10	2	no	—
440	C₂×C₄	—	10	2	no	—
441	C₂×C₄	—	10	1	no	—
442	C₂×C₄	—	10	1	no	—
443	C₂×C₄	—	10	1	no	—
444	C₂×C₄	—	10	1	no	—
445	C₂×C₄	—	10	1	no	—
446	C₂×C₄	—	10	1	no	—
447	C₂×C₄	—	10	1	no	—
448	C₂×C₄	—	10	1	no	—
449	C₂×C₄	—	10	2	no	—
450	C₂×C₄	—	10	2	no	—
451	C₂×C₄	—	20	1	no	—
452	C₂×C₄	—	20	1	no	—
453	C₂×C₄	—	20	1	no	—
454	C₂×C₄	—	20	1	no	—
455	C₂×C₄	—	20	1	no	—
456	C₂×C₄	—	20	1	no	—
457	C₂×C₄	D₅×C₄⋊C₄	1	1	yes	characteristic
458	C₂×C₄	D₅×C₄⋊C₄	1	1	yes	characteristic
459	C₂×C₄	D₅×C₄⋊C₄	1	1	yes	characteristic
460	C₂×C₄	C₂×#676	1	2	yes	—
461	C₂×C₄	D₅×M₁₆	1	2	yes	—
462	C₂×C₄	C₂²×C₄×D₅	1	1	yes	characteristic
463	C₂×C₄	C₂×D₄×D₅	1	1	yes	characteristic
464	C₂×C₄	C₂×Q₈×D₅	1	1	yes	characteristic
465	C₈	—	2	2	no	—
466	C₈	—	4	2	no	—
467	C₈	—	4	1	no	—
468	C₈	—	4	1	no	—
469	C₈	—	5	4	no	—
470	C₈	—	10	2	no	—
471	C₈	—	20	1	no	—
472	C₈	—	20	2	no	—
473	C₈	—	20	1	no	—
474	C₈	C₂×#676	1	4	yes	—
475	C₅	#17797	1	1	yes	characteristic, complemented, Sylow
476	C₂²	—	2	1	no	—
477	C₂²	—	2	1	no	—
478	C₂²	—	5	2	no	—
479	C₂²	—	10	1	no	—
480	C₂²	—	10	1	no	—
481	C₂²	—	10	1	no	—
482	C₂²	—	10	1	no	—
483	C₂²	—	10	1	no	—
484	C₂²	—	20	4	no	—
485	C₂²	#65126	1	2	yes	—
486	C₂²	C₂×D₅×C₄⋊C₄	1	1	yes	characteristic
487	C₄	—	2	1	no	—
488	C₄	—	2	1	no	—
489	C₄	—	2	1	no	—
490	C₄	—	10	1	no	—
491	C₄	—	10	1	no	—
492	C₄	—	10	1	no	—
493	C₄	—	10	1	no	—
494	C₄	—	10	1	no	—
495	C₄	—	10	1	no	—
496	C₄	#65126	1	2	yes	—
497	C₄	C₂²×#676	1	1	yes	characteristic
498	C₄	C₂×D₅×M₁₆	1	1	yes	characteristic
499	C₄	#66107	1	1	yes	characteristic
500	C₄	#66111	1	1	yes	characteristic
501	C₂	—	2	2	no	—
502	C₂	—	10	2	no	—
503	C₂	—	20	1	no	—
504	C₂	C₂×#65126	1	1	yes	characteristic
505	C₂	#10610939	1	1	yes	characteristic
506	C₂	D₅×#430	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×#1565	C₂
socle	C₂²×C₅	C₂²×C₄⋊C₄
prime radical	C₂³×D₅	C₄⋊C₄
cosocle	C₄²×C₅	C₂⁴
hypercenter	#1565	D₅
hypocenter	C₅	#17797
LCS	G ▷ C₂×C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1565

Complements

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

N	H ≅ G/N	type
4. C₅×#1565	C₂	semidirect
5. #10601539	C₂	semidirect
6. #10601213	C₂	semidirect
7. #10600643	C₂	semidirect
8. #10599364	C₂	semidirect
9. #10599363	C₂	semidirect
10. #10599324	C₂	semidirect
11. #10599323	C₂	semidirect
41. C₅×#335	C₂²	semidirect
42. C₅×#334	C₂²	semidirect
43. #64700	C₂²	semidirect
44. #64700	C₂²	semidirect
45. #64699	C₂²	semidirect
46. #64699	C₂²	semidirect
47. #64678	C₂²	semidirect
48. #64677	C₂²	semidirect
119. #1565	D₅	semidirect
145. C₅×M₁₆	M₁₆	semidirect
169. #681	M₁₆	semidirect
214. #335	C₂×D₅	semidirect
218. #334	C₂×D₅	semidirect
386. M₁₆	#676	semidirect
475. C₅	#17797	semidirect

Maximal subgroups

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

subgroup	index
#10611013	2
C₂×#65124	2
C₄×D₅×M₁₆	2
C₅×#1565	2
#10601539	2
#10601213	2
#10600643	2
#10599364	2
#10599363	2
#10599324	2
#10599323	2
#17797	5