Subgroups — #12068787

Order 1280.

714 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	C₅×#2988	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄×#4096	C₂	1	1	yes	maximal, characteristic
3	#10611022	C₂	1	1	yes	maximal, characteristic, complemented
4	#10602432	C₂	1	1	yes	maximal, characteristic, complemented
5	#10601725	C₂	1	2	yes	maximal, complemented
6	C₈×#688	C₂	1	2	yes	maximal, complemented
7	C₈×#687	C₂	1	2	yes	maximal, complemented
8	#10601633	C₂	1	2	yes	maximal, complemented
9	#10601533	C₂	1	1	yes	maximal, characteristic, complemented
10	#10601218	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×#64700	C₂	1	1	yes	maximal, characteristic, complemented
12	C₄×C₅×#41	C₂²	1	1	yes	characteristic
13	C₂×#4096	C₄	1	1	yes	characteristic
14	C₄×#709	C₂²	1	1	yes	characteristic
15	C₅×C₈×Q₈	C₂²	1	2	yes	—
16	C₅×C₈×D₄	—	2	2	no	—
17	C₅×C₈×D₄	C₂²	1	2	yes	—
18	C₅×#431	—	2	1	no	—
19	C₅×#431	C₂²	1	1	yes	characteristic
20	C₂×C₅×C₄⋊C₈	—	2	1	no	—
21	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
22	#65522	C₄	1	1	yes	characteristic
23	C₄×#689	C₄	1	1	yes	characteristic
24	C₄×#689	C₂²	1	1	yes	characteristic
25	C₄×#688	C₄	1	1	yes	characteristic
26	C₄×#688	C₂²	1	1	yes	characteristic
27	C₄×#687	C₄	1	1	yes	characteristic
28	C₄×#687	C₂²	1	1	yes	characteristic
29	C₄×#686	C₄	1	1	yes	characteristic
30	C₄×#686	C₂²	1	1	yes	characteristic
31	#65291	C₄	1	1	yes	characteristic
32	#65287	C₄	1	1	yes	characteristic
33	#65214	C₂²	1	1	yes	characteristic
34	C₂×C₄⋊#168	C₂²	1	1	yes	characteristic
35	C₂×C₄×#168	C₂²	1	1	yes	characteristic
36	#65122	—	2	1	no	—
37	D₅×C₄⋊C₈	—	2	1	no	—
38	#65014	—	2	2	no	—
39	C₈×D₂₀	C₂²	1	2	yes	—
40	C₈×Dic₁₀	C₂²	1	2	yes	—
41	Q₈⋊#168	C₂²	1	2	yes	—
42	D₄⋊#168	C₂²	1	2	yes	—
43	#64704	C₂²	1	2	yes	—
44	#64703	C₂²	1	2	yes	—
45	#64700	C₂²	1	2	yes	—
46	#64700	C₂²	1	2	yes	—
47	#64674	C₂²	1	2	yes	—
48	C₈×#168	C₂²	1	2	yes	—
49	#17858	—	5	1	no	maximal, Sylow
50	C₂×C₅×#41	C₂×C₄	1	1	yes	characteristic
51	C₂×#709	C₂×C₄	1	1	yes	characteristic
52	C₂²×C₅×C₈	—	2	1	no	—
53	C₂²×C₅×C₈	—	2	2	no	—
54	C₄×C₅×Q₈	C₂×C₄	1	1	yes	characteristic
55	C₄×C₅×Q₈	C₂³	1	1	yes	characteristic
56	C₄×C₅×D₄	—	2	1	no	—
57	C₄×C₅×D₄	—	2	1	no	—
58	C₄×C₅×D₄	C₂×C₄	1	1	yes	characteristic
59	C₄×C₅×D₄	C₂³	1	1	yes	characteristic
60	C₅×#117	—	2	1	no	—
61	C₅×#117	C₂×C₄	1	1	yes	characteristic
62	C₂×C₄²×C₅	—	2	1	no	—
63	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
64	#4096	C₈	1	8	yes	complemented
65	C₂×#689	C₂×C₄	1	1	yes	characteristic
66	C₂×#688	C₂×C₄	1	1	yes	characteristic
67	C₂×#687	C₂×C₄	1	1	yes	characteristic
68	C₂×#686	C₂×C₄	1	1	yes	characteristic
69	C₄×C₂²⋊D₅	—	2	1	no	—
70	C₄×C₂²⋊D₅	—	2	1	no	—
71	#4072	C₂×C₄	1	1	yes	characteristic
72	C₂²×#168	—	2	1	no	—
73	C₂²×#168	C₂×C₄	1	1	yes	characteristic
74	C₂²×#168	C₂×C₄	1	1	yes	characteristic
75	C₂×C₈×D₅	—	2	2	no	—
76	C₄×D₂₀	C₂×C₄	1	1	yes	characteristic
77	C₄×D₂₀	C₂³	1	1	yes	characteristic
78	#4018	—	2	1	no	—
79	C₄²×D₅	—	2	1	no	—
80	C₄×Dic₁₀	C₂×C₄	1	1	yes	characteristic
81	C₄×Dic₁₀	C₂³	1	1	yes	characteristic
82	C₅×C₄⋊C₈	—	2	2	no	—
83	C₅×C₄⋊C₈	—	2	1	no	—
84	C₅×C₄⋊C₈	D₄	1	1	yes	characteristic
85	C₅×C₄⋊C₈	D₄	1	1	yes	characteristic
86	C₅×C₄⋊C₈	C₂³	1	2	yes	—
87	C₅×C₂²⋊C₈	—	2	2	no	—
88	C₅×C₂²⋊C₈	D₄	1	2	yes	—
89	C₄×C₅×C₈	—	2	2	no	—
90	C₄×C₅×C₈	C₂³	1	2	yes	—
91	#3967	C₂×C₄	1	1	yes	characteristic
92	#3967	C₂×C₄	1	1	yes	characteristic
93	#3964	C₂×C₄	1	1	yes	characteristic
94	#3964	C₂×C₄	1	1	yes	characteristic
95	C₂²⋊#168	—	2	1	no	—
96	#3952	—	2	2	no	—
97	#3946	—	2	2	no	—
98	C₈×Dic₅	—	2	2	no	—
99	#3942	C₂×C₄	1	1	yes	characteristic
100	#3942	C₂×C₄	1	1	yes	characteristic
101	#3941	C₂×C₄	1	1	yes	characteristic
102	#3941	C₂×C₄	1	1	yes	characteristic
103	#3940	C₂×C₄	1	1	yes	characteristic
104	#3940	C₂×C₄	1	1	yes	characteristic
105	#3939	C₂×C₄	1	1	yes	characteristic
106	#3939	C₂×C₄	1	1	yes	characteristic
107	C₄⋊#168	—	2	1	no	—
108	C₄⋊#168	—	2	1	no	—
109	C₄⋊#168	C₂³	1	2	yes	—
110	C₄×#168	C₂×C₄	1	1	yes	characteristic
111	C₄×#168	C₂×C₄	1	1	yes	characteristic
112	C₄×#168	C₂³	1	2	yes	—
113	C₄×#168	C₂³	1	1	yes	characteristic
114	C₄×#168	C₂³	1	1	yes	characteristic
115	#2988	—	5	1	no	—
116	#2988	D₅	1	1	yes	characteristic, complemented
117	C₄×#135	—	5	1	no	—
118	#1580	—	5	2	no	—
119	#1579	—	5	2	no	—
120	C₈×SD₁₆	—	5	2	no	—
121	C₈×SD₁₆	—	5	2	no	—
122	C₂×#334	—	5	1	no	—
123	#1477	—	5	1	no	—
124	#1477	—	5	1	no	—
125	#1450	—	5	1	no	—
126	C₅×#41	—	2	2	no	—
127	C₅×#41	C₂×C₈	1	4	yes	complemented
128	C₂×C₅×Q₈	C₂²×C₄	1	1	yes	characteristic
129	C₂×C₅×D₄	—	2	1	no	—
130	C₂×C₅×D₄	C₂²×C₄	1	1	yes	characteristic
131	C₂²×C₄×C₅	—	2	1	no	—
132	C₂²×C₄×C₅	—	2	1	no	—
133	C₂²×C₄×C₅	—	2	1	no	—
134	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
135	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
136	C₂²×C₄×C₅	#41	1	1	yes	characteristic
137	C₂×C₂²⋊D₅	—	2	1	no	—
138	#709	—	2	2	no	—
139	#709	C₂×C₈	1	4	yes	complemented
140	C₂×D₂₀	C₂²×C₄	1	1	yes	characteristic
141	C₂×C₄×D₅	—	2	1	no	—
142	C₂×C₄×D₅	—	2	1	no	—
143	C₂×C₄×D₅	—	2	1	no	—
144	C₂×Dic₁₀	C₂²×C₄	1	1	yes	characteristic
145	C₂×C₅×C₈	—	2	2	no	—
146	C₂×C₅×C₈	—	8	2	no	—
147	C₂×C₅×C₈	—	8	1	no	—
148	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
149	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
150	C₅×C₄⋊C₄	—	2	1	no	—
151	C₅×C₄⋊C₄	—	2	1	no	—
152	C₅×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
153	C₅×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
154	C₅×C₂²⋊C₄	—	2	1	no	—
155	C₅×C₂²⋊C₄	—	2	1	no	—
156	C₅×C₂²⋊C₄	—	2	1	no	—
157	C₄²×C₅	—	2	1	no	—
158	C₄²×C₅	—	2	1	no	—
159	C₄²×C₅	—	2	1	no	—
160	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
161	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
162	C₄²×C₅	#41	1	1	yes	characteristic
163	C₄²×C₅	C₂⁴	1	1	yes	characteristic
164	C₂²⋊Dic₅	—	2	1	no	—
165	#689	C₂×C₈	1	4	yes	complemented
166	#688	C₂×C₈	1	4	yes	complemented
167	#687	C₂×C₈	1	4	yes	complemented
168	#686	C₂×C₈	1	4	yes	complemented
169	#685	—	2	1	no	—
170	#685	—	2	1	no	—
171	C₄⋊Dic₅	C₂²×C₄	1	1	yes	characteristic
172	C₄⋊Dic₅	C₂²×C₄	1	1	yes	characteristic
173	#683	—	2	1	no	—
174	#683	—	2	1	no	—
175	C₄×Dic₅	—	2	1	no	—
176	C₄×Dic₅	—	2	1	no	—
177	C₄×Dic₅	—	2	1	no	—
178	C₂×#168	—	2	2	no	—
179	C₂×#168	—	2	2	no	—
180	C₂×#168	—	2	2	no	—
181	C₂×#168	—	8	1	no	—
182	C₂×#168	C₂×C₈	1	4	yes	complemented
183	C₂×#168	C₂²×C₄	1	1	yes	characteristic
184	C₂×#168	C₂²×C₄	1	1	yes	characteristic
185	C₂×#168	C₂²×C₄	1	1	yes	characteristic
186	C₂×#168	C₂²×C₄	1	1	yes	characteristic
187	C₈×D₅	—	8	2	no	—
188	C₂×#135	—	5	1	no	—
189	C₄×#41	—	5	1	no	—
190	C₄×#41	C₂×D₅	1	1	yes	characteristic
191	C₈×Q₈	—	5	2	no	—
192	C₈×Q₈	C₂×D₅	1	2	yes	—
193	C₄×Q₁₆	—	5	1	no	—
194	C₄×Q₁₆	—	5	1	no	—
195	C₄×SD₁₆	—	5	1	no	—
196	C₄×SD₁₆	—	5	1	no	—
197	C₄×SD₁₆	—	5	1	no	—
198	C₄×SD₁₆	—	5	1	no	—
199	C₄×D₈	—	5	1	no	—
200	C₄×D₈	—	5	1	no	—
201	C₈×D₄	—	2	2	no	—
202	C₈×D₄	—	5	2	no	—
203	C₈×D₄	—	10	2	no	—
204	C₈×D₄	C₂×D₅	1	2	yes	—
205	#431	—	2	1	no	—
206	#431	—	5	1	no	—
207	#431	—	10	1	no	—
208	#431	C₂×D₅	1	1	yes	characteristic
209	#427	—	5	1	no	—
210	C₂×C₄⋊C₈	—	2	1	no	—
211	C₂×C₄⋊C₈	—	5	1	no	—
212	C₂×C₄⋊C₈	—	10	1	no	—
213	C₂×C₄⋊C₈	C₂×D₅	1	1	yes	characteristic
214	#416	—	5	1	no	—
215	#416	—	5	1	no	—
216	C₂×C₄×C₈	—	5	1	no	—
217	#334	—	5	2	no	—
218	#334	—	5	2	no	—
219	Q₈⋊C₈	—	5	2	no	—
220	Q₈⋊C₈	—	5	2	no	—
221	D₄⋊C₈	—	5	2	no	—
222	D₄⋊C₈	—	5	2	no	—
223	#322	—	5	2	no	—
224	C₈²	—	5	2	no	—
225	C₂³×C₅	—	2	1	no	—
226	C₂³×C₅	C₄×D₄	1	1	yes	characteristic
227	C₂²×D₅	—	2	1	no	—
228	C₅×Q₈	—	2	1	no	—
229	C₅×Q₈	C₂²×C₈	1	2	yes	—
230	C₅×D₄	—	2	4	no	—
231	C₅×D₄	—	2	1	no	—
232	C₅×D₄	C₂²×C₈	1	2	yes	—
233	C₂×C₄×C₅	—	2	1	no	—
234	C₂×C₄×C₅	—	2	1	no	—
235	C₂×C₄×C₅	—	2	1	no	—
236	C₂×C₄×C₅	—	2	4	no	—
237	C₂×C₄×C₅	—	2	1	no	—
238	C₂×C₄×C₅	—	2	1	no	—
239	C₂×C₄×C₅	—	4	1	no	—
240	C₂×C₄×C₅	—	4	1	no	—
241	C₂×C₄×C₅	—	4	1	no	—
242	C₂×C₄×C₅	—	8	1	no	—
243	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
244	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
245	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
246	C₂×C₄×C₅	C₂²×C₈	1	2	yes	—
247	C₂×C₄×C₅	#131	1	2	yes	—
248	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
249	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
250	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
251	C₂²⋊D₅	—	2	4	no	—
252	C₂×Dic₅	—	2	1	no	—
253	C₂×Dic₅	—	2	1	no	—
254	C₂×Dic₅	—	2	1	no	—
255	D₂₀	—	2	1	no	—
256	D₂₀	C₂²×C₈	1	2	yes	—
257	C₄×D₅	—	2	4	no	—
258	C₄×D₅	—	4	1	no	—
259	C₄×D₅	—	4	1	no	—
260	C₄×D₅	—	8	1	no	—
261	Dic₁₀	—	2	1	no	—
262	Dic₁₀	C₂²×C₈	1	2	yes	—
263	C₅×C₈	—	2	2	no	—
264	C₅×C₈	—	2	2	no	—
265	C₅×C₈	—	4	2	no	—
266	#168	—	2	1	no	—
267	#168	—	2	1	no	—
268	#168	—	4	2	no	—
269	#168	—	4	2	no	—
270	#168	C₂²×C₈	1	2	yes	—
271	#168	C₂²×C₈	1	2	yes	—
272	C₂×#41	—	5	1	no	—
273	C₂×#41	C₄×D₅	1	1	yes	characteristic
274	#135	—	5	8	no	—
275	C₂×Q₁₆	—	5	1	no	—
276	C₂×SD₁₆	—	5	1	no	—
277	C₂×SD₁₆	—	5	1	no	—
278	C₂×D₈	—	5	1	no	—
279	C₂²×C₈	—	2	1	no	—
280	C₂²×C₈	—	2	2	no	—
281	C₂²×C₈	—	5	1	no	—
282	C₂²×C₈	—	5	1	no	—
283	C₂²×C₈	—	10	1	no	—
284	C₂²×C₈	—	10	2	no	—
285	C₄×Q₈	—	5	1	no	—
286	C₄×Q₈	—	5	1	no	—
287	C₄×Q₈	C₄×D₅	1	1	yes	characteristic
288	C₄×Q₈	C₂²×D₅	1	1	yes	characteristic
289	C₄×D₄	—	2	1	no	—
290	C₄×D₄	—	2	1	no	—
291	C₄×D₄	—	5	1	no	—
292	C₄×D₄	—	5	1	no	—
293	C₄×D₄	—	10	1	no	—
294	C₄×D₄	—	10	1	no	—
295	C₄×D₄	C₄×D₅	1	1	yes	characteristic
296	C₄×D₄	C₂²×D₅	1	1	yes	characteristic
297	#117	—	2	1	no	—
298	#117	—	5	1	no	—
299	#117	—	10	1	no	—
300	#117	C₄×D₅	1	1	yes	characteristic
301	C₂×C₄²	—	2	1	no	—
302	C₂×C₄²	—	10	1	no	—
303	C₂×C₄²	C₂²×D₅	1	1	yes	characteristic
304	#107	—	5	1	no	—
305	#107	—	5	1	no	—
306	#106	—	5	1	no	—
307	#106	—	5	1	no	—
308	C₄⋊C₈	—	2	2	no	—
309	C₄⋊C₈	—	2	1	no	—
310	C₄⋊C₈	—	5	2	no	—
311	C₄⋊C₈	—	10	2	no	—
312	C₄⋊C₈	—	10	1	no	—
313	C₄⋊C₈	—	10	1	no	—
314	C₄⋊C₈	C₂²⋊D₅	1	1	yes	characteristic
315	C₄⋊C₈	C₂²⋊D₅	1	1	yes	characteristic
316	C₄⋊C₈	C₂²×D₅	1	2	yes	—
317	#103	—	5	1	no	—
318	#103	—	5	1	no	—
319	#103	—	5	1	no	—
320	#103	—	5	1	no	—
321	#102	—	5	1	no	—
322	#102	—	5	1	no	—
323	#102	—	5	1	no	—
324	#102	—	5	1	no	—
325	C₂²⋊C₈	—	2	2	no	—
326	C₂²⋊C₈	—	10	1	no	—
327	C₂²⋊C₈	—	10	2	no	—
328	C₂²⋊C₈	C₂²⋊D₅	1	2	yes	—
329	C₄×C₈	—	2	2	no	—
330	C₄×C₈	—	5	1	no	—
331	C₄×C₈	—	5	1	no	—
332	C₄×C₈	—	5	1	no	—
333	C₄×C₈	—	5	1	no	—
334	C₄×C₈	—	5	2	no	—
335	C₄×C₈	—	10	2	no	—
336	C₄×C₈	C₂²×D₅	1	2	yes	—
337	C₂²×C₅	—	2	1	no	—
338	C₂²×C₅	—	2	1	no	—
339	C₂²×C₅	—	2	2	no	—
340	C₂²×C₅	—	4	1	no	—
341	C₂²×C₅	—	4	1	no	—
342	C₂²×C₅	C₈×D₄	1	2	yes	—
343	C₂²×C₅	C₂×C₄×D₄	1	1	yes	characteristic
344	C₂×D₅	—	2	2	no	—
345	C₂×D₅	—	4	1	no	—
346	C₂×D₅	—	4	1	no	—
347	C₄×C₅	—	2	2	no	—
348	C₄×C₅	—	2	1	no	—
349	C₄×C₅	—	2	1	no	—
350	C₄×C₅	—	2	1	no	—
351	C₄×C₅	—	4	1	no	—
352	C₄×C₅	—	4	1	no	—
353	C₄×C₅	C₈×D₄	1	2	yes	—
354	C₄×C₅	C₂³×C₈	1	1	yes	characteristic
355	C₄×C₅	C₂×#131	1	1	yes	characteristic
356	C₄×C₅	#577	1	1	yes	characteristic
357	C₄×C₅	#577	1	1	yes	characteristic
358	Dic₅	—	2	2	no	—
359	Dic₅	—	4	1	no	—
360	Dic₅	—	4	1	no	—
361	#41	—	2	2	no	—
362	#41	—	5	4	no	—
363	#41	—	10	2	no	—
364	#41	C₈×D₅	1	4	yes	complemented
365	C₂×Q₈	—	5	1	no	—
366	C₂×Q₈	C₂×C₄×D₅	1	1	yes	characteristic
367	C₂×D₄	—	2	1	no	—
368	C₂×D₄	—	5	1	no	—
369	C₂×D₄	—	10	1	no	—
370	C₂×D₄	C₂×C₄×D₅	1	1	yes	characteristic
371	C₂²×C₄	—	2	1	no	—
372	C₂²×C₄	—	2	1	no	—
373	C₂²×C₄	—	2	1	no	—
374	C₂²×C₄	—	10	1	no	—
375	C₂²×C₄	—	10	1	no	—
376	C₂²×C₄	—	10	1	no	—
377	C₂²×C₄	C₂×C₄×D₅	1	1	yes	characteristic
378	C₂²×C₄	#709	1	1	yes	characteristic
379	C₂²×C₄	C₂×C₂²⋊D₅	1	1	yes	characteristic
380	Q₁₆	—	5	4	no	—
381	SD₁₆	—	5	4	no	—
382	SD₁₆	—	5	4	no	—
383	D₈	—	5	4	no	—
384	C₂×C₈	—	2	2	no	—
385	C₂×C₈	—	5	1	no	—
386	C₂×C₈	—	5	1	no	—
387	C₂×C₈	—	5	4	no	—
388	C₂×C₈	—	5	1	no	—
389	C₂×C₈	—	5	1	no	—
390	C₂×C₈	—	8	2	no	—
391	C₂×C₈	—	8	1	no	—
392	C₂×C₈	—	10	2	no	—
393	C₂×C₈	—	10	2	no	—
394	C₂×C₈	—	10	2	no	—
395	C₂×C₈	—	40	2	no	—
396	C₂×C₈	—	40	1	no	—
397	C₂×C₈	C₂×C₂²⋊D₅	1	2	yes	—
398	C₂×C₈	C₂×C₂²⋊D₅	1	2	yes	—
399	C₄⋊C₄	—	2	1	no	—
400	C₄⋊C₄	—	2	1	no	—
401	C₄⋊C₄	—	5	1	no	—
402	C₄⋊C₄	—	5	1	no	—
403	C₄⋊C₄	—	10	1	no	—
404	C₄⋊C₄	—	10	1	no	—
405	C₄⋊C₄	C₂×C₄×D₅	1	1	yes	characteristic
406	C₄⋊C₄	C₂×C₄×D₅	1	1	yes	characteristic
407	C₂²⋊C₄	—	2	1	no	—
408	C₂²⋊C₄	—	2	1	no	—
409	C₂²⋊C₄	—	2	1	no	—
410	C₂²⋊C₄	—	10	1	no	—
411	C₂²⋊C₄	—	10	1	no	—
412	C₂²⋊C₄	—	10	1	no	—
413	C₄²	—	2	1	no	—
414	C₄²	—	2	1	no	—
415	C₄²	—	2	1	no	—
416	C₄²	—	10	1	no	—
417	C₄²	—	10	1	no	—
418	C₄²	—	10	1	no	—
419	C₄²	C₂×C₄×D₅	1	1	yes	characteristic
420	C₄²	#709	1	1	yes	characteristic
421	C₄²	C₂×C₂²⋊D₅	1	1	yes	characteristic
422	C₄²	C₂³×D₅	1	1	yes	characteristic
423	C₂×C₅	—	2	2	no	—
424	C₂×C₅	—	4	2	no	—
425	C₂×C₅	C₂×C₈×D₄	1	1	yes	characteristic
426	C₂×C₅	#2952	1	1	yes	characteristic
427	C₂×C₅	#2957	1	1	yes	characteristic
428	D₅	—	4	2	no	—
429	C₂³	—	2	1	no	—
430	C₂³	—	10	1	no	—
431	C₂³	C₄×C₂²⋊D₅	1	1	yes	characteristic
432	Q₈	—	2	1	no	—
433	Q₈	—	5	2	no	—
434	Q₈	—	10	1	no	—
435	Q₈	C₂×C₈×D₅	1	2	yes	—
436	D₄	—	2	4	no	—
437	D₄	—	2	1	no	—
438	D₄	—	5	2	no	—
439	D₄	—	10	4	no	—
440	D₄	—	10	1	no	—
441	D₄	C₂×C₈×D₅	1	2	yes	—
442	C₂×C₄	—	2	1	no	—
443	C₂×C₄	—	2	4	no	—
444	C₂×C₄	—	2	1	no	—
445	C₂×C₄	—	2	1	no	—
446	C₂×C₄	—	2	1	no	—
447	C₂×C₄	—	2	1	no	—
448	C₂×C₄	—	4	1	no	—
449	C₂×C₄	—	4	1	no	—
450	C₂×C₄	—	4	1	no	—
451	C₂×C₄	—	8	1	no	—
452	C₂×C₄	—	10	1	no	—
453	C₂×C₄	—	10	4	no	—
454	C₂×C₄	—	10	1	no	—
455	C₂×C₄	—	10	1	no	—
456	C₂×C₄	—	20	1	no	—
457	C₂×C₄	—	20	1	no	—
458	C₂×C₄	—	40	1	no	—
459	C₂×C₄	C₂×C₈×D₅	1	2	yes	—
460	C₂×C₄	#4047	1	2	yes	—
461	C₂×C₄	C₄×C₂²⋊D₅	1	1	yes	characteristic
462	C₂×C₄	C₄×C₂²⋊D₅	1	1	yes	characteristic
463	C₂×C₄	C₄×C₂²⋊D₅	1	1	yes	characteristic
464	C₂×C₄	C₂²×C₄×D₅	1	1	yes	characteristic
465	C₂×C₄	C₂×#709	1	1	yes	characteristic
466	C₂×C₄	C₂²×C₂²⋊D₅	1	1	yes	characteristic
467	C₈	—	2	2	no	—
468	C₈	—	2	2	no	—
469	C₈	—	4	2	no	—
470	C₈	—	5	2	no	—
471	C₈	—	5	2	no	—
472	C₈	—	10	1	no	—
473	C₈	—	10	1	no	—
474	C₈	—	20	2	no	—
475	C₈	—	20	2	no	—
476	C₅	#17858	1	1	yes	characteristic, complemented, Sylow
477	C₂²	—	2	1	no	—
478	C₂²	—	2	1	no	—
479	C₂²	—	2	2	no	—
480	C₂²	—	4	1	no	—
481	C₂²	—	4	1	no	—
482	C₂²	—	10	2	no	—
483	C₂²	—	20	1	no	—
484	C₂²	—	20	1	no	—
485	C₂²	C₈×C₂²⋊D₅	1	2	yes	—
486	C₂²	C₂×C₄×C₂²⋊D₅	1	1	yes	characteristic
487	C₄	—	2	1	no	—
488	C₄	—	2	2	no	—
489	C₄	—	2	1	no	—
490	C₄	—	2	1	no	—
491	C₄	—	4	1	no	—
492	C₄	—	4	1	no	—
493	C₄	—	10	2	no	—
494	C₄	—	20	1	no	—
495	C₄	—	20	1	no	—
496	C₄	C₈×C₂²⋊D₅	1	2	yes	—
497	C₄	C₂²×C₈×D₅	1	1	yes	characteristic
498	C₄	C₂×#4047	1	1	yes	characteristic
499	C₄	#66170	1	1	yes	characteristic
500	C₄	#66171	1	1	yes	characteristic
501	C₂	—	2	2	no	—
502	C₂	—	4	2	no	—
503	C₂	—	20	2	no	—
504	C₂	#10614289	1	1	yes	characteristic
505	C₂	C₂×C₈×C₂²⋊D₅	1	1	yes	characteristic
506	C₂	#10615543	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×C₂²⋊D₅
commutator	C₄×C₅	C₂³×C₈
Frattini	C₄²	C₂³×D₅
Fitting	C₅×#2988	C₂
socle	C₂²×C₅	C₂×C₄×D₄
prime radical	C₂×#4096	C₄
cosocle	C₄²×C₅	C₂⁴
hypercenter	#2988	D₅
hypocenter	C₅	#17858
LCS	G ▷ C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₄ ◁ #431 ◁ #2988

Complements

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

N	H ≅ G/N	type
1. C₅×#2988	C₂	semidirect
3. #10611022	C₂	semidirect
4. #10602432	C₂	semidirect
5. #10601725	C₂	semidirect
6. C₈×#688	C₂	semidirect
7. C₈×#687	C₂	semidirect
8. #10601633	C₂	semidirect
9. #10601533	C₂	semidirect
10. #10601218	C₂	semidirect
11. C₂×#64700	C₂	semidirect
64. #4096	C₈	semidirect
116. #2988	D₅	semidirect
127. C₅×#41	C₂×C₈	semidirect
139. #709	C₂×C₈	semidirect
165. #689	C₂×C₈	semidirect
166. #688	C₂×C₈	semidirect
167. #687	C₂×C₈	semidirect
168. #686	C₂×C₈	semidirect
182. C₂×#168	C₂×C₈	semidirect
364. #41	C₈×D₅	semidirect
476. C₅	#17858	semidirect

Maximal subgroups

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

subgroup	index
C₅×#2988	2
C₄×#4096	2
#10611022	2
#10602432	2
#10601725	2
C₈×#688	2
C₈×#687	2
#10601633	2
#10601533	2
#10601218	2
C₂×#64700	2
#17858	5