Subgroups — #12068435

Order 1280.

602 conjugacy classes of subgroups.

The subgroup lattice has 510 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#10611070	C₂	1	1	yes	maximal, characteristic
2	#10611014	C₂	1	1	yes	maximal, characteristic
3	#10610744	C₂	1	1	yes	maximal, characteristic
4	C₅×#1573	C₂	1	1	yes	maximal, characteristic, complemented
5	#10601589	C₂	1	1	yes	maximal, characteristic, complemented
6	#10601546	C₂	1	1	yes	maximal, characteristic, complemented
7	#10601215	C₂	1	1	yes	maximal, characteristic, complemented
8	#10599368	C₂	1	1	yes	maximal, characteristic, complemented
9	#10599365	C₂	1	1	yes	maximal, characteristic, complemented
10	#10599361	C₂	1	1	yes	maximal, characteristic, complemented
11	D₅×#335	C₂	1	1	yes	maximal, characteristic, complemented
12	#10599327	C₂	1	1	yes	maximal, characteristic, complemented
13	#10599326	C₂	1	1	yes	maximal, characteristic, complemented
14	#10599321	C₂	1	1	yes	maximal, characteristic, complemented
15	#10599320	C₂	1	1	yes	maximal, characteristic, complemented
16	C₄×#709	C₂²	1	1	yes	characteristic
17	C₅×#432	C₂²	1	1	yes	characteristic
18	C₅×#431	C₂²	1	1	yes	characteristic
19	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
20	C₈×C₂²⋊D₅	—	2	1	no	—
21	C₈×C₂²⋊D₅	—	2	1	no	—
22	#65214	C₂²	1	1	yes	characteristic
23	#65214	C₂²	1	1	yes	characteristic
24	#65213	C₂²	1	1	yes	characteristic
25	#65129	C₄	1	2	yes	—
26	#65128	C₄	1	2	yes	—
27	#65126	C₂²	1	1	yes	characteristic
28	#65124	C₂²	1	1	yes	characteristic
29	#65123	—	2	1	no	—
30	#65122	C₂²	1	1	yes	characteristic
31	#65122	C₂²	1	1	yes	characteristic
32	#65122	C₂²	1	1	yes	characteristic
33	D₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
34	D₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
35	D₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
36	#65119	—	2	1	no	—
37	#65018	—	2	1	no	—
38	#65017	—	2	1	no	—
39	#65016	C₄	1	2	yes	—
40	#65009	C₄	1	2	yes	—
41	#64995	—	2	1	no	—
42	#64990	—	2	1	no	—
43	C₄×#676	C₂²	1	1	yes	characteristic
44	#64974	C₂²	1	1	yes	characteristic
45	#64974	C₂²	1	1	yes	characteristic
46	C₄×C₈×D₅	C₂²	1	1	yes	characteristic
47	C₅×#335	C₂²	1	1	yes	characteristic
48	C₅×#335	C₂²	1	1	yes	characteristic
49	C₅×#334	C₂²	1	1	yes	characteristic
50	C₅×#334	C₂²	1	1	yes	characteristic
51	#64700	C₂²	1	1	yes	characteristic
52	#64700	C₂²	1	1	yes	characteristic
53	#64699	C₂²	1	1	yes	characteristic
54	#64699	C₂²	1	1	yes	characteristic
55	#64699	C₂²	1	1	yes	characteristic
56	#64699	C₂²	1	1	yes	characteristic
57	#64699	C₂²	1	1	yes	characteristic
58	#64699	C₂²	1	1	yes	characteristic
59	#64678	C₂²	1	1	yes	characteristic
60	#64678	C₂²	1	1	yes	characteristic
61	#64677	C₂²	1	1	yes	characteristic
62	#64677	C₂²	1	1	yes	characteristic
63	#17812	—	5	1	no	maximal, Sylow
64	C₂×#709	C₂×C₄	1	1	yes	characteristic
65	C₂²×C₅×C₈	—	2	1	no	—
66	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
67	C₄×C₂²⋊D₅	D₄	1	1	yes	characteristic
68	C₄×C₂²⋊D₅	D₄	1	1	yes	characteristic
69	C₄×C₂²⋊D₅	Q₈	1	1	yes	characteristic
70	C₄×C₂²⋊D₅	Q₈	1	1	yes	characteristic
71	#4072	C₂×C₄	1	1	yes	characteristic
72	C₂×#681	—	2	1	no	—
73	C₂×#676	—	2	1	no	—
74	C₂×#676	C₂×C₄	1	2	yes	—
75	C₂×C₈×D₅	—	2	1	no	—
76	C₂×C₈×D₅	—	2	1	no	—
77	C₂×C₈×D₅	—	2	1	no	—
78	C₂×C₈×D₅	C₂×C₄	1	2	yes	—
79	C₄×D₂₀	D₄	1	1	yes	characteristic
80	C₄×D₂₀	Q₈	1	1	yes	characteristic
81	#4018	C₂×C₄	1	1	yes	characteristic
82	#4018	C₂×C₄	1	1	yes	characteristic
83	C₄²×D₅	C₂³	1	1	yes	characteristic
84	C₄²×D₅	C₂³	1	1	yes	characteristic
85	C₄×Dic₁₀	D₄	1	1	yes	characteristic
86	C₄×Dic₁₀	Q₈	1	1	yes	characteristic
87	C₅×C₄⋊C₈	—	2	1	no	—
88	C₅×C₄⋊C₈	C₂×C₄	1	2	yes	—
89	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
90	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
91	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
92	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
93	C₅×C₂²⋊C₈	—	2	1	no	—
94	C₅×C₂²⋊C₈	C₂×C₄	1	2	yes	—
95	C₅×#97	—	2	1	no	—
96	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
97	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
98	C₂²⋊#168	—	2	1	no	—
99	C₂²⋊#168	C₂×C₄	1	2	yes	—
100	#3952	—	2	1	no	—
101	#3952	—	2	1	no	—
102	#3952	—	2	1	no	—
103	#3952	—	2	1	no	—
104	#3952	C₂×C₄	1	2	yes	—
105	#3952	C₂×C₄	1	2	yes	—
106	#3947	—	2	1	no	—
107	#3947	C₂×C₄	1	2	yes	—
108	#3946	—	2	1	no	—
109	#3946	—	2	1	no	—
110	#3946	—	2	1	no	—
111	#3946	—	2	1	no	—
112	#3946	C₂×C₄	1	2	yes	—
113	#3946	C₂×C₄	1	2	yes	—
114	C₈×Dic₅	—	2	1	no	—
115	C₈×Dic₅	—	2	1	no	—
116	C₈×Dic₅	—	2	1	no	—
117	C₈×Dic₅	C₂×C₄	1	2	yes	—
118	C₄⋊#168	—	2	1	no	—
119	C₄⋊#168	C₂×C₄	1	2	yes	—
120	C₄⋊#168	C₂³	1	1	yes	characteristic
121	C₄⋊#168	C₂³	1	1	yes	characteristic
122	C₄⋊#168	C₂³	1	1	yes	characteristic
123	C₄⋊#168	C₂³	1	1	yes	characteristic
124	C₄×#168	—	2	1	no	—
125	C₄×#168	C₂³	1	1	yes	characteristic
126	C₄×#168	C₂³	1	1	yes	characteristic
127	#2989	—	5	1	no	—
128	#2988	—	5	1	no	—
129	#2922	—	5	1	no	—
130	#1574	—	5	1	no	—
131	#1574	—	5	1	no	—
132	#1573	—	5	1	no	—
133	#1573	D₅	1	1	yes	characteristic, complemented
134	#1572	—	5	1	no	—
135	#1572	—	5	1	no	—
136	#1571	—	5	1	no	—
137	#1571	—	5	1	no	—
138	#1565	—	5	1	no	—
139	#1565	—	5	1	no	—
140	#1564	—	5	1	no	—
141	C₂×#335	—	5	1	no	—
142	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
143	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
144	C₂²×C₄×C₅	C₂×Q₈	1	1	yes	characteristic
145	C₂×C₂²⋊D₅	C₄⋊C₄	1	1	yes	characteristic
146	C₂×C₂²⋊D₅	C₄⋊C₄	1	1	yes	characteristic
147	#709	—	2	4	no	—
148	C₂×D₂₀	C₄⋊C₄	1	1	yes	characteristic
149	C₂×C₄×D₅	C₂²×C₄	1	1	yes	characteristic
150	C₂×C₄×D₅	C₂²×C₄	1	1	yes	characteristic
151	C₂×C₄×D₅	C₂×D₄	1	1	yes	characteristic
152	C₂×C₄×D₅	C₂×D₄	1	1	yes	characteristic
153	C₂×C₄×D₅	C₂×Q₈	1	1	yes	characteristic
154	C₂×C₄×D₅	C₂×Q₈	1	1	yes	characteristic
155	C₂×Dic₁₀	C₄⋊C₄	1	1	yes	characteristic
156	C₂×C₅×C₈	—	2	1	no	—
157	C₂×C₅×C₈	—	2	1	no	—
158	C₂×C₅×C₈	—	2	1	no	—
159	C₂×C₅×C₈	—	2	1	no	—
160	C₂×C₅×C₈	—	8	1	no	—
161	C₂×C₅×C₈	C₂²×C₄	1	2	yes	—
162	C₂×C₅×C₈	C₂²×C₄	1	2	yes	—
163	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
164	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
165	C₄²×C₅	C₂×Q₈	1	1	yes	characteristic
166	C₄²×C₅	C₂⁴	1	1	yes	characteristic
167	C₂²⋊Dic₅	C₄⋊C₄	1	1	yes	characteristic
168	C₂²⋊Dic₅	C₄⋊C₄	1	1	yes	characteristic
169	#685	C₄⋊C₄	1	1	yes	characteristic
170	#685	C₄⋊C₄	1	1	yes	characteristic
171	#685	C₄⋊C₄	1	1	yes	characteristic
172	#685	C₄⋊C₄	1	1	yes	characteristic
173	C₄⋊Dic₅	C₄⋊C₄	1	1	yes	characteristic
174	C₄⋊Dic₅	C₄⋊C₄	1	1	yes	characteristic
175	#683	C₄⋊C₄	1	1	yes	characteristic
176	#683	C₄⋊C₄	1	1	yes	characteristic
177	#683	C₄⋊C₄	1	1	yes	characteristic
178	#683	C₄⋊C₄	1	1	yes	characteristic
179	C₄×Dic₅	C₂²×C₄	1	1	yes	characteristic
180	C₄×Dic₅	C₂²×C₄	1	1	yes	characteristic
181	C₄×Dic₅	C₂×D₄	1	1	yes	characteristic
182	C₄×Dic₅	C₂×D₄	1	1	yes	characteristic
183	C₄×Dic₅	C₂×Q₈	1	1	yes	characteristic
184	C₄×Dic₅	C₂×Q₈	1	1	yes	characteristic
185	#681	—	8	1	no	—
186	C₂×#168	—	2	1	no	—
187	C₂×#168	—	2	1	no	—
188	C₂×#168	—	2	1	no	—
189	C₂×#168	—	2	1	no	—
190	C₂×#168	C₂²×C₄	1	2	yes	—
191	C₂×#168	C₂²×C₄	1	2	yes	—
192	#676	—	2	4	no	—
193	#676	—	8	1	no	—
194	C₈×D₅	—	2	4	no	—
195	C₈×D₅	—	8	1	no	—
196	C₈×D₅	—	8	1	no	—
197	C₈×D₅	—	8	1	no	—
198	C₄×#41	—	5	1	no	—
199	#446	—	10	1	no	—
200	C₈×Q₈	—	10	1	no	—
201	#436	—	10	1	no	—
202	#435	—	10	1	no	—
203	#435	—	10	1	no	—
204	C₈×D₄	—	10	1	no	—
205	C₈×D₄	—	10	1	no	—
206	C₈×D₄	—	10	1	no	—
207	#433	—	5	2	no	—
208	#433	—	5	2	no	—
209	#432	—	5	1	no	—
210	#432	C₂×D₅	1	1	yes	characteristic
211	#431	—	5	1	no	—
212	#431	—	5	1	no	—
213	#431	—	5	1	no	—
214	#431	—	5	1	no	—
215	#431	—	5	1	no	—
216	#431	—	5	1	no	—
217	#431	—	5	1	no	—
218	#431	C₂×D₅	1	1	yes	characteristic
219	#424	—	5	2	no	—
220	#423	—	5	1	no	—
221	#423	—	5	1	no	—
222	C₂×C₄⋊C₈	—	5	1	no	—
223	C₂×C₄⋊C₈	—	5	1	no	—
224	C₂×C₄⋊C₈	—	5	1	no	—
225	C₂×C₄⋊C₈	C₂×D₅	1	1	yes	characteristic
226	#408	—	5	2	no	—
227	C₄×M₁₆	—	5	1	no	—
228	C₂×C₄×C₈	—	5	1	no	—
229	#335	—	5	1	no	—
230	#335	—	5	1	no	—
231	#335	—	5	1	no	—
232	#335	—	5	1	no	—
233	#335	—	5	1	no	—
234	#335	—	5	1	no	—
235	#335	—	5	1	no	—
236	#335	—	5	1	no	—
237	#335	C₂×D₅	1	1	yes	characteristic
238	#335	C₂×D₅	1	1	yes	characteristic
239	#334	—	5	1	no	—
240	#334	—	5	1	no	—
241	#334	—	5	1	no	—
242	#334	—	5	1	no	—
243	#334	C₂×D₅	1	1	yes	characteristic
244	#334	C₂×D₅	1	1	yes	characteristic
245	C₂³×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
246	C₂²×D₅	C₂×C₄⋊C₄	1	1	yes	characteristic
247	C₂²×D₅	C₂×C₄⋊C₄	1	1	yes	characteristic
248	C₂×C₄×C₅	—	2	2	no	—
249	C₂×C₄×C₅	—	2	1	no	—
250	C₂×C₄×C₅	—	2	1	no	—
251	C₂×C₄×C₅	—	4	1	no	—
252	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
253	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
254	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
255	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
256	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
257	C₂×C₄×C₅	C₂²×Q₈	1	1	yes	characteristic
258	C₂²⋊D₅	—	2	2	no	—
259	C₂²⋊D₅	—	2	2	no	—
260	C₂×Dic₅	C₂×C₄⋊C₄	1	1	yes	characteristic
261	C₂×Dic₅	C₂×C₄⋊C₄	1	1	yes	characteristic
262	C₂×Dic₅	C₂×C₄⋊C₄	1	1	yes	characteristic
263	C₂×Dic₅	C₂×C₄⋊C₄	1	1	yes	characteristic
264	C₂×Dic₅	C₂×C₄⋊C₄	1	1	yes	characteristic
265	C₂×Dic₅	C₂×C₄⋊C₄	1	1	yes	characteristic
266	D₂₀	—	2	2	no	—
267	C₄×D₅	—	2	2	no	—
268	C₄×D₅	—	2	1	no	—
269	C₄×D₅	—	2	1	no	—
270	C₄×D₅	—	2	1	no	—
271	C₄×D₅	—	2	1	no	—
272	C₄×D₅	—	4	1	no	—
273	C₄×D₅	—	4	1	no	—
274	C₄×D₅	#131	1	4	yes	—
275	Dic₁₀	—	2	2	no	—
276	C₅×C₈	—	2	2	no	—
277	C₅×C₈	—	2	2	no	—
278	C₅×C₈	—	4	1	no	—
279	C₅×C₈	—	4	1	no	—
280	C₅×C₈	—	4	1	no	—
281	C₅×C₈	—	4	1	no	—
282	#168	—	2	2	no	—
283	#168	—	2	2	no	—
284	#168	—	4	1	no	—
285	#168	—	4	1	no	—
286	#168	—	4	1	no	—
287	#168	—	4	1	no	—
288	C₂×#41	—	5	1	no	—
289	C₂×M₁₆	—	5	2	no	—
290	C₂×M₁₆	—	10	1	no	—
291	C₂×M₁₆	—	10	1	no	—
292	C₂²×C₈	—	2	1	no	—
293	C₂²×C₈	—	5	2	no	—
294	C₂²×C₈	—	10	1	no	—
295	C₂²×C₈	—	10	1	no	—
296	C₂²×C₈	—	10	1	no	—
297	C₄×Q₈	—	5	1	no	—
298	C₄×Q₈	—	5	1	no	—
299	C₄×D₄	—	5	1	no	—
300	C₄×D₄	—	5	1	no	—
301	C₄×D₄	—	5	1	no	—
302	C₄×D₄	—	5	1	no	—
303	C₄×D₄	—	5	1	no	—
304	C₄×D₄	—	5	1	no	—
305	#117	—	5	1	no	—
306	#117	—	5	1	no	—
307	#117	—	5	1	no	—
308	C₂×C₄²	—	5	1	no	—
309	C₂×C₄²	—	5	1	no	—
310	C₂×C₄²	C₂²×D₅	1	1	yes	characteristic
311	C₄⋊C₈	—	2	1	no	—
312	C₄⋊C₈	—	5	2	no	—
313	C₄⋊C₈	—	5	2	no	—
314	C₄⋊C₈	—	5	2	no	—
315	C₄⋊C₈	—	5	1	no	—
316	C₄⋊C₈	—	5	1	no	—
317	C₄⋊C₈	—	5	1	no	—
318	C₄⋊C₈	—	5	1	no	—
319	C₄⋊C₈	—	10	1	no	—
320	C₄⋊C₈	—	10	1	no	—
321	C₄⋊C₈	—	10	1	no	—
322	C₄⋊C₈	—	10	1	no	—
323	C₄⋊C₈	—	10	1	no	—
324	C₄⋊C₈	C₄×D₅	1	2	yes	—
325	C₄⋊C₈	C₂²×D₅	1	1	yes	characteristic
326	C₄⋊C₈	C₂²×D₅	1	1	yes	characteristic
327	C₄⋊C₈	C₂²×D₅	1	1	yes	characteristic
328	C₄⋊C₈	C₂²×D₅	1	1	yes	characteristic
329	C₂²⋊C₈	—	2	1	no	—
330	C₂²⋊C₈	—	5	2	no	—
331	C₂²⋊C₈	—	5	2	no	—
332	C₂²⋊C₈	—	5	2	no	—
333	C₂²⋊C₈	—	10	1	no	—
334	C₂²⋊C₈	—	10	1	no	—
335	C₂²⋊C₈	—	10	1	no	—
336	C₂²⋊C₈	—	10	1	no	—
337	C₂²⋊C₈	—	10	1	no	—
338	C₂²⋊C₈	C₄×D₅	1	2	yes	—
339	#97	—	2	1	no	—
340	#97	—	5	2	no	—
341	#97	—	10	1	no	—
342	C₄×C₈	—	5	2	no	—
343	C₄×C₈	—	5	1	no	—
344	C₄×C₈	—	5	1	no	—
345	C₄×C₈	—	10	1	no	—
346	C₄×C₈	—	10	1	no	—
347	C₄×C₈	—	10	1	no	—
348	C₄×C₈	—	10	1	no	—
349	C₄×C₈	C₂²×D₅	1	1	yes	characteristic
350	C₄×C₈	C₂²×D₅	1	1	yes	characteristic
351	C₂²×C₅	—	2	1	no	—
352	C₂²×C₅	—	2	1	no	—
353	C₂²×C₅	—	2	1	no	—
354	C₂²×C₅	C₂²×C₄⋊C₄	1	1	yes	characteristic
355	C₂×D₅	—	2	1	no	—
356	C₂×D₅	—	2	1	no	—
357	C₂×D₅	—	2	1	no	—
358	C₂×D₅	—	2	1	no	—
359	C₂×D₅	—	2	1	no	—
360	C₂×D₅	#424	1	2	yes	—
361	C₄×C₅	—	2	1	no	—
362	C₄×C₅	—	2	1	no	—
363	C₄×C₅	—	2	1	no	—
364	C₄×C₅	—	2	1	no	—
365	C₄×C₅	C₂×#131	1	2	yes	—
366	C₄×C₅	#576	1	1	yes	characteristic
367	C₄×C₅	#578	1	1	yes	characteristic
368	Dic₅	—	2	1	no	—
369	Dic₅	—	2	1	no	—
370	Dic₅	—	2	1	no	—
371	Dic₅	—	2	1	no	—
372	Dic₅	—	2	1	no	—
373	Dic₅	#424	1	2	yes	—
374	#41	—	10	4	no	—
375	C₂×Q₈	—	5	1	no	—
376	C₂×D₄	—	5	1	no	—
377	C₂×D₄	—	5	1	no	—
378	C₂×D₄	—	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	C₂×C₄×D₅	1	1	yes	characteristic
386	C₂²×C₄	D₄×D₅	1	1	yes	characteristic
387	C₂²×C₄	Q₈×D₅	1	1	yes	characteristic
388	M₁₆	—	10	4	no	—
389	M₁₆	—	40	1	no	—
390	M₁₆	—	40	1	no	—
391	C₂×C₈	—	2	1	no	—
392	C₂×C₈	—	2	1	no	—
393	C₂×C₈	—	2	1	no	—
394	C₂×C₈	—	2	1	no	—
395	C₂×C₈	—	5	2	no	—
396	C₂×C₈	—	5	2	no	—
397	C₂×C₈	—	8	1	no	—
398	C₂×C₈	—	10	4	no	—
399	C₂×C₈	—	10	1	no	—
400	C₂×C₈	—	10	1	no	—
401	C₂×C₈	—	10	1	no	—
402	C₂×C₈	—	10	1	no	—
403	C₂×C₈	—	40	1	no	—
404	C₂×C₈	—	40	1	no	—
405	C₂×C₈	—	40	1	no	—
406	C₂×C₈	C₂×C₄×D₅	1	2	yes	—
407	C₂×C₈	C₂×C₄×D₅	1	2	yes	—
408	C₄⋊C₄	—	5	1	no	—
409	C₄⋊C₄	—	5	1	no	—
410	C₄⋊C₄	—	5	1	no	—
411	C₄⋊C₄	—	5	1	no	—
412	C₄⋊C₄	—	5	1	no	—
413	C₄⋊C₄	—	5	1	no	—
414	C₂²⋊C₄	—	5	1	no	—
415	C₂²⋊C₄	—	5	1	no	—
416	C₂²⋊C₄	—	5	1	no	—
417	C₂²⋊C₄	—	5	1	no	—
418	C₂²⋊C₄	—	5	1	no	—
419	C₂²⋊C₄	—	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	D₄×D₅	1	1	yes	characteristic
428	C₄²	Q₈×D₅	1	1	yes	characteristic
429	C₄²	C₂³×D₅	1	1	yes	characteristic
430	C₂×C₅	—	4	1	no	—
431	C₂×C₅	C₂×#424	1	1	yes	characteristic
432	C₂×C₅	#2913	1	1	yes	characteristic
433	C₂×C₅	#2916	1	1	yes	characteristic
434	D₅	—	2	2	no	—
435	D₅	—	4	1	no	—
436	C₂³	—	5	1	no	—
437	C₂³	—	5	1	no	—
438	C₂³	D₅×C₄⋊C₄	1	1	yes	characteristic
439	Q₈	—	10	2	no	—
440	D₄	—	10	2	no	—
441	D₄	—	10	2	no	—
442	D₄	—	10	2	no	—
443	C₂×C₄	—	2	2	no	—
444	C₂×C₄	—	2	1	no	—
445	C₂×C₄	—	2	1	no	—
446	C₂×C₄	—	4	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	—	5	1	no	—
454	C₂×C₄	—	10	2	no	—
455	C₂×C₄	—	10	1	no	—
456	C₂×C₄	—	10	1	no	—
457	C₂×C₄	—	10	1	no	—
458	C₂×C₄	—	10	1	no	—
459	C₂×C₄	—	20	1	no	—
460	C₂×C₄	—	20	1	no	—
461	C₂×C₄	D₅×C₄⋊C₄	1	1	yes	characteristic
462	C₂×C₄	D₅×C₄⋊C₄	1	1	yes	characteristic
463	C₂×C₄	D₅×C₄⋊C₄	1	1	yes	characteristic
464	C₂×C₄	C₂²×C₄×D₅	1	1	yes	characteristic
465	C₂×C₄	C₂×D₄×D₅	1	1	yes	characteristic
466	C₂×C₄	C₂×Q₈×D₅	1	1	yes	characteristic
467	C₈	—	2	2	no	—
468	C₈	—	2	2	no	—
469	C₈	—	4	1	no	—
470	C₈	—	4	1	no	—
471	C₈	—	4	1	no	—
472	C₈	—	4	1	no	—
473	C₈	—	10	2	no	—
474	C₈	—	10	2	no	—
475	C₈	—	20	1	no	—
476	C₈	—	20	1	no	—
477	C₈	—	20	1	no	—
478	C₈	—	20	1	no	—
479	C₅	#17812	1	1	yes	characteristic, complemented, Sylow
480	C₂²	—	2	1	no	—
481	C₂²	—	2	1	no	—
482	C₂²	—	2	1	no	—
483	C₂²	—	5	2	no	—
484	C₂²	—	10	1	no	—
485	C₂²	—	10	1	no	—
486	C₂²	—	10	1	no	—
487	C₂²	—	10	1	no	—
488	C₂²	—	10	1	no	—
489	C₂²	C₂×D₅×C₄⋊C₄	1	1	yes	characteristic
490	C₄	—	2	1	no	—
491	C₄	—	2	1	no	—
492	C₄	—	2	1	no	—
493	C₄	—	2	1	no	—
494	C₄	—	5	2	no	—
495	C₄	—	10	1	no	—
496	C₄	—	10	1	no	—
497	C₄	—	10	1	no	—
498	C₄	—	10	1	no	—
499	C₄	—	10	1	no	—
500	C₄	D₅×#131	1	2	yes	—
501	C₄	#66108	1	1	yes	characteristic
502	C₄	#66113	1	1	yes	characteristic
503	C₂	—	4	1	no	—
504	C₂	—	10	2	no	—
505	C₂	—	20	1	no	—
506	C₂	D₅×#424	1	1	yes	characteristic
507	C₂	#10610941	1	1	yes	characteristic
508	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×#1573	C₂
socle	C₂²×C₅	C₂²×C₄⋊C₄
prime radical	C₂×#709	C₂×C₄
cosocle	C₄²×C₅	C₂⁴
hypercenter	#1573	D₅
hypocenter	C₅	#17812
LCS	G ▷ C₂×C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1573

Complements

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

N	H ≅ G/N	type
4. C₅×#1573	C₂	semidirect
5. #10601589	C₂	semidirect
6. #10601546	C₂	semidirect
7. #10601215	C₂	semidirect
8. #10599368	C₂	semidirect
9. #10599365	C₂	semidirect
10. #10599361	C₂	semidirect
11. D₅×#335	C₂	semidirect
12. #10599327	C₂	semidirect
13. #10599326	C₂	semidirect
14. #10599321	C₂	semidirect
15. #10599320	C₂	semidirect
133. #1573	D₅	semidirect
479. C₅	#17812	semidirect

Maximal subgroups

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

subgroup	index
#10611070	2
#10611014	2
#10610744	2
C₅×#1573	2
#10601589	2
#10601546	2
#10601215	2
#10599368	2
#10599365	2
#10599361	2
D₅×#335	2
#10599327	2
#10599326	2
#10599321	2
#10599320	2
#17812	5