Subgroups — #12068539

Order 1280.

610 conjugacy classes of subgroups.

The subgroup lattice has 480 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#10611016	C₂	1	2	yes	maximal
2	C₈×#709	C₂	1	1	yes	maximal, characteristic
3	C₅×#1564	C₂	1	1	yes	maximal, characteristic, complemented
4	#10601540	C₂	1	2	yes	maximal, complemented
5	#10600525	C₂	1	1	yes	maximal, characteristic, complemented
6	#10599363	C₂	1	1	yes	maximal, characteristic, complemented
7	#10599362	C₂	1	1	yes	maximal, characteristic, complemented
8	#10599360	C₂	1	1	yes	maximal, characteristic, complemented
9	D₅×#335	C₂	1	1	yes	maximal, characteristic, complemented
10	#10599326	C₂	1	2	yes	maximal, complemented
11	#10599325	C₂	1	2	yes	maximal, complemented
12	C₄×#709	C₂²	1	1	yes	characteristic
13	C₅×#431	C₂²	1	2	yes	—
14	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
15	C₈×C₂²⋊D₅	C₄	1	1	yes	characteristic
16	C₈×C₂²⋊D₅	C₄	1	1	yes	characteristic
17	C₈×C₂²⋊D₅	C₄	1	1	yes	characteristic
18	C₈×C₂²⋊D₅	C₄	1	1	yes	characteristic
19	#65215	C₂²	1	2	yes	—
20	#65214	C₂²	1	1	yes	characteristic
21	#65126	C₂²	1	2	yes	—
22	#65124	C₂²	1	2	yes	—
23	#65122	C₂²	1	2	yes	—
24	D₅×C₄⋊C₈	C₂²	1	2	yes	—
25	#65016	—	2	2	no	—
26	#65009	—	2	2	no	—
27	#64979	—	2	2	no	—
28	#64978	—	2	2	no	—
29	C₈×D₂₀	C₄	1	1	yes	characteristic
30	C₈×D₂₀	C₄	1	1	yes	characteristic
31	#64974	C₂²	1	1	yes	characteristic
32	#64974	C₂²	1	1	yes	characteristic
33	C₄×C₈×D₅	C₂²	1	1	yes	characteristic
34	C₄×C₈×D₅	C₂²	1	1	yes	characteristic
35	C₈×Dic₁₀	C₄	1	1	yes	characteristic
36	C₈×Dic₁₀	C₄	1	1	yes	characteristic
37	C₅×#335	C₂²	1	1	yes	characteristic
38	C₅×#335	C₂²	1	1	yes	characteristic
39	C₅×#334	C₂²	1	2	yes	—
40	#64700	C₂²	1	2	yes	—
41	#64700	C₂²	1	2	yes	—
42	#64699	C₂²	1	2	yes	—
43	#64699	C₂²	1	2	yes	—
44	#64678	C₂²	1	1	yes	characteristic
45	#64678	C₂²	1	1	yes	characteristic
46	#64677	C₂²	1	2	yes	—
47	#17829	—	5	1	no	maximal, Sylow
48	C₂×#709	D₄	1	1	yes	characteristic
49	C₂²×C₅×C₈	C₂×C₄	1	1	yes	characteristic
50	C₂²×C₅×C₈	C₂×C₄	1	1	yes	characteristic
51	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
52	C₄×C₂²⋊D₅	C₂×C₄	1	1	yes	characteristic
53	C₄×C₂²⋊D₅	C₂×C₄	1	1	yes	characteristic
54	C₄×C₂²⋊D₅	Q₈	1	1	yes	characteristic
55	C₄×C₂²⋊D₅	Q₈	1	1	yes	characteristic
56	#4072	D₄	1	1	yes	characteristic
57	C₂×#676	—	2	2	no	—
58	C₂×C₈×D₅	—	2	2	no	—
59	C₂×C₈×D₅	C₂×C₄	1	1	yes	characteristic
60	C₂×C₈×D₅	C₂×C₄	1	1	yes	characteristic
61	C₂×C₈×D₅	C₂×C₄	1	1	yes	characteristic
62	C₂×C₈×D₅	C₂×C₄	1	1	yes	characteristic
63	C₄×D₂₀	C₂×C₄	1	1	yes	characteristic
64	C₄×D₂₀	Q₈	1	1	yes	characteristic
65	#4018	D₄	1	1	yes	characteristic
66	#4018	D₄	1	1	yes	characteristic
67	C₄²×D₅	C₂³	1	1	yes	characteristic
68	C₄²×D₅	C₂³	1	1	yes	characteristic
69	C₄×Dic₁₀	C₂×C₄	1	1	yes	characteristic
70	C₄×Dic₁₀	Q₈	1	1	yes	characteristic
71	C₅×C₄⋊C₈	C₂³	1	2	yes	—
72	C₅×C₄⋊C₈	C₂³	1	2	yes	—
73	C₅×C₂²⋊C₈	—	2	2	no	—
74	C₄×C₅×C₈	—	2	2	no	—
75	C₄×C₅×C₈	C₂×C₄	1	1	yes	characteristic
76	C₄×C₅×C₈	C₂×C₄	1	1	yes	characteristic
77	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
78	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
79	C₂²⋊#168	—	2	2	no	—
80	C₂²⋊#168	C₂×C₄	1	1	yes	characteristic
81	C₂²⋊#168	C₂×C₄	1	1	yes	characteristic
82	#3952	—	2	2	no	—
83	#3952	—	2	2	no	—
84	#3952	C₂×C₄	1	1	yes	characteristic
85	#3952	C₂×C₄	1	1	yes	characteristic
86	#3952	C₂×C₄	1	1	yes	characteristic
87	#3952	C₂×C₄	1	1	yes	characteristic
88	#3947	—	2	2	no	—
89	#3946	—	2	2	no	—
90	#3946	—	2	2	no	—
91	#3946	C₂×C₄	1	1	yes	characteristic
92	#3946	C₂×C₄	1	1	yes	characteristic
93	#3946	C₂×C₄	1	1	yes	characteristic
94	#3946	C₂×C₄	1	1	yes	characteristic
95	C₈×Dic₅	—	2	2	no	—
96	C₈×Dic₅	C₂×C₄	1	1	yes	characteristic
97	C₈×Dic₅	C₂×C₄	1	1	yes	characteristic
98	C₈×Dic₅	C₂×C₄	1	1	yes	characteristic
99	C₈×Dic₅	C₂×C₄	1	1	yes	characteristic
100	C₄⋊#168	C₂×C₄	1	1	yes	characteristic
101	C₄⋊#168	C₂×C₄	1	1	yes	characteristic
102	C₄⋊#168	C₂³	1	2	yes	—
103	C₄⋊#168	C₂³	1	2	yes	—
104	#3935	—	2	2	no	—
105	C₄×#168	C₂³	1	1	yes	characteristic
106	C₄×#168	C₂³	1	1	yes	characteristic
107	C₈×#41	—	5	1	no	—
108	#2925	—	5	2	no	—
109	#1572	—	5	2	no	—
110	#1572	—	5	2	no	—
111	#1570	—	5	2	no	—
112	#1568	—	5	1	no	—
113	#1568	—	5	1	no	—
114	#1567	—	5	1	no	—
115	#1564	—	5	1	no	—
116	#1564	D₅	1	1	yes	characteristic, complemented
117	C₂×#335	—	5	1	no	—
118	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
119	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
120	C₂²×C₄×C₅	C₂×Q₈	1	1	yes	characteristic
121	C₂×C₂²⋊D₅	C₄⋊C₄	1	1	yes	characteristic
122	C₂×C₂²⋊D₅	C₄⋊C₄	1	1	yes	characteristic
123	#709	—	2	2	no	—
124	#709	—	2	2	no	—
125	C₂×D₂₀	C₄⋊C₄	1	1	yes	characteristic
126	C₂×C₄×D₅	C₂²×C₄	1	1	yes	characteristic
127	C₂×C₄×D₅	C₂²×C₄	1	1	yes	characteristic
128	C₂×C₄×D₅	C₂×D₄	1	1	yes	characteristic
129	C₂×C₄×D₅	C₂×D₄	1	1	yes	characteristic
130	C₂×C₄×D₅	C₂×Q₈	1	1	yes	characteristic
131	C₂×C₄×D₅	C₂×Q₈	1	1	yes	characteristic
132	C₂×Dic₁₀	C₄⋊C₄	1	1	yes	characteristic
133	C₂×C₅×C₈	—	2	2	no	—
134	C₂×C₅×C₈	—	2	2	no	—
135	C₂×C₅×C₈	—	2	2	no	—
136	C₂×C₅×C₈	—	4	1	no	—
137	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
138	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
139	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
140	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
141	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
142	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
143	C₄²×C₅	C₂×Q₈	1	1	yes	characteristic
144	C₄²×C₅	C₂⁴	1	1	yes	characteristic
145	C₂²⋊Dic₅	C₄⋊C₄	1	1	yes	characteristic
146	C₂²⋊Dic₅	C₄⋊C₄	1	1	yes	characteristic
147	#685	C₄⋊C₄	1	1	yes	characteristic
148	#685	C₄⋊C₄	1	1	yes	characteristic
149	#685	C₄⋊C₄	1	1	yes	characteristic
150	#685	C₄⋊C₄	1	1	yes	characteristic
151	C₄⋊Dic₅	C₄⋊C₄	1	1	yes	characteristic
152	C₄⋊Dic₅	C₄⋊C₄	1	1	yes	characteristic
153	#683	C₄⋊C₄	1	1	yes	characteristic
154	#683	C₄⋊C₄	1	1	yes	characteristic
155	#683	C₄⋊C₄	1	1	yes	characteristic
156	#683	C₄⋊C₄	1	1	yes	characteristic
157	C₄×Dic₅	C₂²×C₄	1	1	yes	characteristic
158	C₄×Dic₅	C₂²×C₄	1	1	yes	characteristic
159	C₄×Dic₅	C₂×D₄	1	1	yes	characteristic
160	C₄×Dic₅	C₂×D₄	1	1	yes	characteristic
161	C₄×Dic₅	C₂×Q₈	1	1	yes	characteristic
162	C₄×Dic₅	C₂×Q₈	1	1	yes	characteristic
163	C₂×#168	—	2	2	no	—
164	C₂×#168	—	2	2	no	—
165	C₂×#168	C₂²×C₄	1	1	yes	characteristic
166	C₂×#168	C₂²×C₄	1	1	yes	characteristic
167	C₂×#168	C₂²×C₄	1	1	yes	characteristic
168	C₂×#168	C₂²×C₄	1	1	yes	characteristic
169	#676	—	4	4	no	—
170	C₈×D₅	—	2	2	no	—
171	C₈×D₅	—	2	2	no	—
172	C₈×D₅	—	4	1	no	—
173	C₈×D₅	—	4	1	no	—
174	C₈×D₅	—	4	4	no	—
175	C₄×#41	—	5	1	no	—
176	C₈×Q₈	—	5	1	no	—
177	C₈×Q₈	—	5	1	no	—
178	C₈×D₄	—	5	1	no	—
179	C₈×D₄	—	5	1	no	—
180	C₈×D₄	—	5	1	no	—
181	C₈×D₄	—	5	1	no	—
182	C₈×D₄	—	5	1	no	—
183	C₈×D₄	—	5	1	no	—
184	#433	—	10	2	no	—
185	#433	—	10	2	no	—
186	#432	—	5	2	no	—
187	#432	—	5	2	no	—
188	#431	—	5	1	no	—
189	#431	—	5	1	no	—
190	#431	—	5	1	no	—
191	#431	—	5	2	no	—
192	#431	C₂×D₅	1	2	yes	—
193	#423	—	5	2	no	—
194	C₂×C₄⋊C₈	—	5	2	no	—
195	#408	—	10	2	no	—
196	#405	—	10	2	no	—
197	C₂×C₄×C₈	—	5	1	no	—
198	C₂×C₄×C₈	—	5	1	no	—
199	C₂×C₄×C₈	C₂×D₅	1	1	yes	characteristic
200	#335	—	5	2	no	—
201	#335	—	5	2	no	—
202	#335	—	5	1	no	—
203	#335	—	5	1	no	—
204	#335	C₂×D₅	1	1	yes	characteristic
205	#335	C₂×D₅	1	1	yes	characteristic
206	#334	—	5	2	no	—
207	#334	—	5	2	no	—
208	#334	—	5	2	no	—
209	#334	C₂×D₅	1	2	yes	—
210	C₂³×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
211	C₂²×D₅	C₂×C₄⋊C₄	1	1	yes	characteristic
212	C₂²×D₅	C₂×C₄⋊C₄	1	1	yes	characteristic
213	C₂×C₄×C₅	—	2	1	no	—
214	C₂×C₄×C₅	—	2	1	no	—
215	C₂×C₄×C₅	—	2	1	no	—
216	C₂×C₄×C₅	—	2	1	no	—
217	C₂×C₄×C₅	—	4	1	no	—
218	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
219	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
220	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
221	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
222	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
223	C₂×C₄×C₅	C₂²×Q₈	1	1	yes	characteristic
224	C₂²⋊D₅	—	2	2	no	—
225	C₂²⋊D₅	—	2	2	no	—
226	C₂×Dic₅	C₂×C₄⋊C₄	1	1	yes	characteristic
227	C₂×Dic₅	C₂×C₄⋊C₄	1	1	yes	characteristic
228	C₂×Dic₅	C₂×C₄⋊C₄	1	1	yes	characteristic
229	C₂×Dic₅	C₂×C₄⋊C₄	1	1	yes	characteristic
230	C₂×Dic₅	C₂×C₄⋊C₄	1	1	yes	characteristic
231	C₂×Dic₅	C₂×C₄⋊C₄	1	1	yes	characteristic
232	D₂₀	—	2	2	no	—
233	C₄×D₅	—	2	1	no	—
234	C₄×D₅	—	2	1	no	—
235	C₄×D₅	—	2	1	no	—
236	C₄×D₅	—	2	1	no	—
237	C₄×D₅	—	2	1	no	—
238	C₄×D₅	—	2	1	no	—
239	C₄×D₅	—	4	1	no	—
240	C₄×D₅	—	4	1	no	—
241	C₄×D₅	#135	1	2	yes	—
242	C₄×D₅	#135	1	2	yes	—
243	Dic₁₀	—	2	2	no	—
244	C₅×C₈	—	2	1	no	—
245	C₅×C₈	—	2	1	no	—
246	C₅×C₈	—	2	1	no	—
247	C₅×C₈	—	4	2	no	—
248	C₅×C₈	—	4	2	no	—
249	C₅×C₈	#131	1	2	yes	—
250	#168	—	2	1	no	—
251	#168	—	2	1	no	—
252	#168	—	2	1	no	—
253	#168	—	2	1	no	—
254	#168	—	4	2	no	—
255	#168	—	4	2	no	—
256	C₂×#41	—	5	1	no	—
257	C₂×M₁₆	—	10	2	no	—
258	C₂²×C₈	—	5	1	no	—
259	C₂²×C₈	—	5	1	no	—
260	C₂²×C₈	—	5	1	no	—
261	C₂²×C₈	—	5	1	no	—
262	C₂²×C₈	—	10	2	no	—
263	C₂²×C₈	C₄×D₅	1	1	yes	characteristic
264	C₂²×C₈	C₄×D₅	1	1	yes	characteristic
265	C₄×Q₈	—	5	1	no	—
266	C₄×Q₈	—	5	1	no	—
267	C₄×D₄	—	5	1	no	—
268	C₄×D₄	—	5	1	no	—
269	C₄×D₄	—	5	1	no	—
270	C₄×D₄	—	5	1	no	—
271	C₄×D₄	—	5	1	no	—
272	C₄×D₄	—	5	1	no	—
273	#117	—	5	1	no	—
274	#117	—	5	1	no	—
275	#117	—	5	1	no	—
276	C₂×C₄²	—	5	1	no	—
277	C₂×C₄²	—	5	1	no	—
278	C₂×C₄²	C₂²×D₅	1	1	yes	characteristic
279	C₄⋊C₈	—	5	1	no	—
280	C₄⋊C₈	—	5	1	no	—
281	C₄⋊C₈	—	5	1	no	—
282	C₄⋊C₈	—	5	1	no	—
283	C₄⋊C₈	—	5	1	no	—
284	C₄⋊C₈	—	5	1	no	—
285	C₄⋊C₈	—	5	2	no	—
286	C₄⋊C₈	—	5	2	no	—
287	C₄⋊C₈	—	10	2	no	—
288	C₄⋊C₈	—	10	2	no	—
289	C₄⋊C₈	C₂²×D₅	1	2	yes	—
290	C₄⋊C₈	C₂²×D₅	1	2	yes	—
291	C₂²⋊C₈	—	2	2	no	—
292	C₂²⋊C₈	—	5	1	no	—
293	C₂²⋊C₈	—	5	1	no	—
294	C₂²⋊C₈	—	5	1	no	—
295	C₂²⋊C₈	—	5	1	no	—
296	C₂²⋊C₈	—	5	1	no	—
297	C₂²⋊C₈	—	5	1	no	—
298	C₂²⋊C₈	—	10	2	no	—
299	C₂²⋊C₈	—	10	2	no	—
300	C₂²⋊C₈	—	10	2	no	—
301	#97	—	10	2	no	—
302	#97	—	10	2	no	—
303	C₄×C₈	—	2	2	no	—
304	C₄×C₈	—	5	1	no	—
305	C₄×C₈	—	5	1	no	—
306	C₄×C₈	—	5	1	no	—
307	C₄×C₈	—	5	1	no	—
308	C₄×C₈	—	5	1	no	—
309	C₄×C₈	—	5	1	no	—
310	C₄×C₈	—	10	2	no	—
311	C₄×C₈	C₄×D₅	1	1	yes	characteristic
312	C₄×C₈	C₄×D₅	1	1	yes	characteristic
313	C₄×C₈	C₂²×D₅	1	1	yes	characteristic
314	C₄×C₈	C₂²×D₅	1	1	yes	characteristic
315	C₂²×C₅	—	2	1	no	—
316	C₂²×C₅	—	2	1	no	—
317	C₂²×C₅	—	2	1	no	—
318	C₂²×C₅	C₂²×C₄⋊C₄	1	1	yes	characteristic
319	C₂×D₅	—	2	1	no	—
320	C₂×D₅	—	2	1	no	—
321	C₂×D₅	—	2	1	no	—
322	C₂×D₅	—	2	1	no	—
323	C₂×D₅	—	2	1	no	—
324	C₂×D₅	#427	1	2	yes	—
325	C₄×C₅	—	2	1	no	—
326	C₄×C₅	—	2	1	no	—
327	C₄×C₅	—	2	1	no	—
328	C₄×C₅	—	2	1	no	—
329	C₄×C₅	C₂×#131	1	1	yes	characteristic
330	C₄×C₅	#568	1	1	yes	characteristic
331	C₄×C₅	C₂×#135	1	1	yes	characteristic
332	C₄×C₅	C₂×#135	1	1	yes	characteristic
333	Dic₅	—	2	1	no	—
334	Dic₅	—	2	1	no	—
335	Dic₅	—	2	1	no	—
336	Dic₅	—	2	1	no	—
337	Dic₅	—	2	1	no	—
338	Dic₅	#427	1	2	yes	—
339	#41	—	10	2	no	—
340	#41	—	10	2	no	—
341	C₂×Q₈	—	5	1	no	—
342	C₂×D₄	—	5	1	no	—
343	C₂×D₄	—	5	1	no	—
344	C₂×D₄	—	5	1	no	—
345	C₂²×C₄	—	5	1	no	—
346	C₂²×C₄	—	5	1	no	—
347	C₂²×C₄	—	5	1	no	—
348	C₂²×C₄	—	5	1	no	—
349	C₂²×C₄	—	5	1	no	—
350	C₂²×C₄	—	5	1	no	—
351	C₂²×C₄	C₂×C₄×D₅	1	1	yes	characteristic
352	C₂²×C₄	D₄×D₅	1	1	yes	characteristic
353	C₂²×C₄	Q₈×D₅	1	1	yes	characteristic
354	M₁₆	—	20	4	no	—
355	C₂×C₈	—	2	2	no	—
356	C₂×C₈	—	2	2	no	—
357	C₂×C₈	—	2	2	no	—
358	C₂×C₈	—	4	1	no	—
359	C₂×C₈	—	5	1	no	—
360	C₂×C₈	—	5	1	no	—
361	C₂×C₈	—	5	1	no	—
362	C₂×C₈	—	5	1	no	—
363	C₂×C₈	—	10	2	no	—
364	C₂×C₈	—	10	2	no	—
365	C₂×C₈	—	10	2	no	—
366	C₂×C₈	—	10	2	no	—
367	C₂×C₈	—	20	1	no	—
368	C₂×C₈	—	20	1	no	—
369	C₂×C₈	—	20	4	no	—
370	C₂×C₈	C₂×C₄×D₅	1	1	yes	characteristic
371	C₂×C₈	C₂×C₄×D₅	1	1	yes	characteristic
372	C₂×C₈	C₂×C₄×D₅	1	1	yes	characteristic
373	C₂×C₈	C₂×C₄×D₅	1	1	yes	characteristic
374	C₄⋊C₄	—	5	1	no	—
375	C₄⋊C₄	—	5	1	no	—
376	C₄⋊C₄	—	5	1	no	—
377	C₄⋊C₄	—	5	1	no	—
378	C₄⋊C₄	—	5	1	no	—
379	C₄⋊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	C₄²	—	5	1	no	—
387	C₄²	—	5	1	no	—
388	C₄²	—	5	1	no	—
389	C₄²	—	5	1	no	—
390	C₄²	—	5	1	no	—
391	C₄²	—	5	1	no	—
392	C₄²	C₂×C₄×D₅	1	1	yes	characteristic
393	C₄²	D₄×D₅	1	1	yes	characteristic
394	C₄²	Q₈×D₅	1	1	yes	characteristic
395	C₄²	C₂³×D₅	1	1	yes	characteristic
396	C₂×C₅	—	4	1	no	—
397	C₂×C₅	#2906	1	1	yes	characteristic
398	C₂×C₅	C₂×#427	1	1	yes	characteristic
399	C₂×C₅	#2916	1	1	yes	characteristic
400	D₅	—	2	2	no	—
401	D₅	—	4	1	no	—
402	C₂³	—	5	1	no	—
403	C₂³	—	5	1	no	—
404	C₂³	D₅×C₄⋊C₄	1	1	yes	characteristic
405	Q₈	—	10	2	no	—
406	D₄	—	10	2	no	—
407	D₄	—	10	2	no	—
408	D₄	—	10	2	no	—
409	C₂×C₄	—	2	1	no	—
410	C₂×C₄	—	2	1	no	—
411	C₂×C₄	—	2	1	no	—
412	C₂×C₄	—	2	1	no	—
413	C₂×C₄	—	4	1	no	—
414	C₂×C₄	—	5	1	no	—
415	C₂×C₄	—	5	2	no	—
416	C₂×C₄	—	5	2	no	—
417	C₂×C₄	—	5	1	no	—
418	C₂×C₄	—	5	1	no	—
419	C₂×C₄	—	5	1	no	—
420	C₂×C₄	—	5	1	no	—
421	C₂×C₄	—	5	1	no	—
422	C₂×C₄	—	10	1	no	—
423	C₂×C₄	—	10	1	no	—
424	C₂×C₄	—	10	1	no	—
425	C₂×C₄	—	10	1	no	—
426	C₂×C₄	—	10	1	no	—
427	C₂×C₄	—	10	1	no	—
428	C₂×C₄	—	20	1	no	—
429	C₂×C₄	—	20	1	no	—
430	C₂×C₄	D₅×C₄⋊C₄	1	1	yes	characteristic
431	C₂×C₄	D₅×C₄⋊C₄	1	1	yes	characteristic
432	C₂×C₄	D₅×C₄⋊C₄	1	1	yes	characteristic
433	C₂×C₄	C₂²×C₄×D₅	1	1	yes	characteristic
434	C₂×C₄	C₂×D₄×D₅	1	1	yes	characteristic
435	C₂×C₄	C₂×Q₈×D₅	1	1	yes	characteristic
436	C₈	—	2	1	no	—
437	C₈	—	2	1	no	—
438	C₈	—	2	1	no	—
439	C₈	—	4	2	no	—
440	C₈	—	4	2	no	—
441	C₈	—	10	1	no	—
442	C₈	—	10	1	no	—
443	C₈	—	10	1	no	—
444	C₈	—	10	1	no	—
445	C₈	—	20	2	no	—
446	C₈	—	20	2	no	—
447	C₈	#4047	1	2	yes	—
448	C₅	#17829	1	1	yes	characteristic, complemented, Sylow
449	C₂²	—	2	1	no	—
450	C₂²	—	2	1	no	—
451	C₂²	—	2	1	no	—
452	C₂²	—	5	2	no	—
453	C₂²	—	10	1	no	—
454	C₂²	—	10	1	no	—
455	C₂²	—	10	1	no	—
456	C₂²	—	10	1	no	—
457	C₂²	—	10	1	no	—
458	C₂²	C₂×D₅×C₄⋊C₄	1	1	yes	characteristic
459	C₄	—	2	1	no	—
460	C₄	—	2	1	no	—
461	C₄	—	2	1	no	—
462	C₄	—	2	1	no	—
463	C₄	—	5	2	no	—
464	C₄	—	10	1	no	—
465	C₄	—	10	1	no	—
466	C₄	—	10	1	no	—
467	C₄	—	10	1	no	—
468	C₄	—	10	1	no	—
469	C₄	C₂×#4047	1	1	yes	characteristic
470	C₄	#66079	1	1	yes	characteristic
471	C₄	D₅×#135	1	1	yes	characteristic
472	C₄	D₅×#135	1	1	yes	characteristic
473	C₂	—	4	1	no	—
474	C₂	—	10	2	no	—
475	C₂	—	20	1	no	—
476	C₂	#10610743	1	1	yes	characteristic
477	C₂	D₅×#427	1	1	yes	characteristic
478	C₂	#10610983	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×#1564	C₂
socle	C₂²×C₅	C₂²×C₄⋊C₄
prime radical	C₂×#709	D₄
cosocle	C₄²×C₅	C₂⁴
hypercenter	#1564	D₅
hypocenter	C₅	#17829
LCS	G ▷ C₂×C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1564

Complements

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

N	H ≅ G/N	type
3. C₅×#1564	C₂	semidirect
4. #10601540	C₂	semidirect
5. #10600525	C₂	semidirect
6. #10599363	C₂	semidirect
7. #10599362	C₂	semidirect
8. #10599360	C₂	semidirect
9. D₅×#335	C₂	semidirect
10. #10599326	C₂	semidirect
11. #10599325	C₂	semidirect
116. #1564	D₅	semidirect
448. C₅	#17829	semidirect

Maximal subgroups

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

subgroup	index
#10611016	2
C₈×#709	2
C₅×#1564	2
#10601540	2
#10600525	2
#10599363	2
#10599362	2
#10599360	2
D₅×#335	2
#10599326	2
#10599325	2
#17829	5