Subgroups — #12070321

Order 1280.

608 conjugacy classes of subgroups.

The subgroup lattice has 582 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#2971	C₂	1	1	yes	maximal, characteristic, complemented
2	#10614259	C₂	1	1	yes	maximal, characteristic
3	#10610242	C₂	1	1	yes	maximal, characteristic, complemented
4	#10602431	C₂	1	1	yes	maximal, characteristic, complemented
5	#10601730	C₂	1	1	yes	maximal, characteristic, complemented
6	#10601729	C₂	1	1	yes	maximal, characteristic, complemented
7	#10601728	C₂	1	1	yes	maximal, characteristic, complemented
8	#10601725	C₂	1	1	yes	maximal, characteristic, complemented
9	#10601658	C₂	1	1	yes	maximal, characteristic, complemented
10	#10601656	C₂	1	1	yes	maximal, characteristic, complemented
11	#10601654	C₂	1	1	yes	maximal, characteristic, complemented
12	#10601653	C₂	1	1	yes	maximal, characteristic, complemented
13	#10601593	C₂	1	1	yes	maximal, characteristic, complemented
14	#10601589	C₂	1	1	yes	maximal, characteristic, complemented
15	#10600640	C₂	1	1	yes	maximal, characteristic, complemented
16	C₄×C₅×#41	C₂²	1	1	yes	characteristic
17	#65813	C₂²	1	1	yes	characteristic
18	C₅×C₈×Q₈	C₂²	1	1	yes	characteristic
19	C₅×C₈×Q₈	C₂²	1	1	yes	characteristic
20	C₅×#436	—	2	1	no	—
21	C₅×#436	—	2	1	no	—
22	C₅×#436	C₂²	1	1	yes	characteristic
23	C₅×#436	C₂²	1	1	yes	characteristic
24	C₅×#432	—	2	1	no	—
25	C₅×#432	C₂²	1	1	yes	characteristic
26	C₄×C₅×M₁₆	—	2	1	no	—
27	C₄×C₅×M₁₆	C₂²	1	1	yes	characteristic
28	#65528	C₄	1	1	yes	characteristic
29	#65527	C₄	1	1	yes	characteristic
30	#65417	—	2	1	no	—
31	#65416	—	2	1	no	—
32	C₄×#689	C₂²	1	1	yes	characteristic
33	#65317	C₄	1	1	yes	characteristic
34	C₄×#688	C₂²	1	1	yes	characteristic
35	#65311	C₄	1	1	yes	characteristic
36	C₄×#687	C₂²	1	1	yes	characteristic
37	#65305	C₄	1	1	yes	characteristic
38	C₄×#686	C₂²	1	1	yes	characteristic
39	#65298	C₄	1	1	yes	characteristic
40	#65292	C₄	1	1	yes	characteristic
41	#65285	C₄	1	1	yes	characteristic
42	#65214	C₂²	1	1	yes	characteristic
43	#65214	C₂²	1	1	yes	characteristic
44	C₂×C₄×#168	C₂²	1	1	yes	characteristic
45	#64998	—	2	1	no	—
46	#64997	—	2	1	no	—
47	#64977	C₂²	1	1	yes	characteristic
48	C₈×D₂₀	C₂²	1	1	yes	characteristic
49	#64968	C₂²	1	1	yes	characteristic
50	C₈×Dic₁₀	C₂²	1	1	yes	characteristic
51	Q₈⋊#168	C₂²	1	1	yes	characteristic
52	Q₈⋊#168	C₂²	1	1	yes	characteristic
53	D₄⋊#168	C₂²	1	1	yes	characteristic
54	D₄⋊#168	C₂²	1	1	yes	characteristic
55	#64704	C₂²	1	1	yes	characteristic
56	#64704	C₂²	1	1	yes	characteristic
57	#64703	C₂²	1	1	yes	characteristic
58	#64703	C₂²	1	1	yes	characteristic
59	#64700	C₂²	1	1	yes	characteristic
60	#64700	C₂²	1	1	yes	characteristic
61	#64699	C₂²	1	1	yes	characteristic
62	#64699	C₂²	1	1	yes	characteristic
63	#64674	C₂²	1	1	yes	characteristic
64	#64674	C₂²	1	1	yes	characteristic
65	#64674	C₂²	1	1	yes	characteristic
66	#64674	C₂²	1	1	yes	characteristic
67	#18005	—	5	1	no	maximal, Sylow
68	C₂×C₅×#41	C₂×C₄	1	1	yes	characteristic
69	C₂×C₅×M₁₆	—	2	1	no	—
70	C₂×C₅×M₁₆	—	2	1	no	—
71	C₂×C₅×M₁₆	D₄	1	1	yes	characteristic
72	C₂×C₅×M₁₆	D₄	1	1	yes	characteristic
73	C₄×C₅×Q₈	C₂×C₄	1	1	yes	characteristic
74	C₄×C₅×Q₈	C₂³	1	1	yes	characteristic
75	C₄×C₅×D₄	—	2	1	no	—
76	C₄×C₅×D₄	—	2	1	no	—
77	C₄×C₅×D₄	C₂×C₄	1	1	yes	characteristic
78	C₄×C₅×D₄	C₂³	1	1	yes	characteristic
79	C₅×#117	—	2	1	no	—
80	C₅×#117	C₂×C₄	1	1	yes	characteristic
81	C₂×C₄²×C₅	—	2	1	no	—
82	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
83	C₂×#689	C₂×C₄	1	1	yes	characteristic
84	C₂×#688	C₂×C₄	1	1	yes	characteristic
85	C₂×#687	C₂×C₄	1	1	yes	characteristic
86	C₂×#686	C₂×C₄	1	1	yes	characteristic
87	#4076	C₂×C₄	1	1	yes	characteristic
88	#4075	—	2	1	no	—
89	C₄×C₂²⋊D₅	—	2	1	no	—
90	#4070	C₂×C₄	1	1	yes	characteristic
91	C₂²×#168	—	2	1	no	—
92	C₂×#676	—	2	1	no	—
93	C₂×C₈×D₅	—	2	1	no	—
94	#4022	—	2	1	no	—
95	#4021	C₂×C₄	1	1	yes	characteristic
96	C₄×D₂₀	C₂³	1	1	yes	characteristic
97	#4018	—	2	1	no	—
98	#4016	C₂×C₄	1	1	yes	characteristic
99	C₄×Dic₁₀	C₂³	1	1	yes	characteristic
100	C₅×C₄⋊C₈	—	2	1	no	—
101	C₅×C₄⋊C₈	—	2	1	no	—
102	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
103	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
104	C₅×C₂²⋊C₈	—	2	1	no	—
105	C₅×C₂²⋊C₈	—	2	1	no	—
106	C₅×C₂²⋊C₈	—	2	1	no	—
107	C₅×#97	—	2	1	no	—
108	C₅×#97	D₄	1	1	yes	characteristic
109	C₅×#97	D₄	1	1	yes	characteristic
110	C₄×C₅×C₈	—	2	1	no	—
111	C₄×C₅×C₈	—	2	1	no	—
112	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
113	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
114	#3967	C₂×C₄	1	1	yes	characteristic
115	#3967	C₂×C₄	1	1	yes	characteristic
116	#3964	C₂×C₄	1	1	yes	characteristic
117	#3964	C₂×C₄	1	1	yes	characteristic
118	C₂²⋊#168	—	2	1	no	—
119	C₂²⋊#168	C₂×C₄	1	1	yes	characteristic
120	C₂²⋊#168	C₂×C₄	1	1	yes	characteristic
121	#3952	—	2	1	no	—
122	#3952	—	2	1	no	—
123	#3947	—	2	1	no	—
124	#3946	—	2	1	no	—
125	#3946	—	2	1	no	—
126	C₈×Dic₅	—	2	1	no	—
127	#3942	C₂×C₄	1	1	yes	characteristic
128	#3942	C₂×C₄	1	1	yes	characteristic
129	#3941	C₂×C₄	1	1	yes	characteristic
130	#3941	C₂×C₄	1	1	yes	characteristic
131	#3940	C₂×C₄	1	1	yes	characteristic
132	#3940	C₂×C₄	1	1	yes	characteristic
133	#3939	C₂×C₄	1	1	yes	characteristic
134	#3939	C₂×C₄	1	1	yes	characteristic
135	C₄⋊#168	C₂×C₄	1	1	yes	characteristic
136	C₄⋊#168	C₂×C₄	1	1	yes	characteristic
137	C₄⋊#168	C₂³	1	1	yes	characteristic
138	C₄⋊#168	C₂³	1	1	yes	characteristic
139	C₄×#168	—	2	1	no	—
140	C₄×#168	—	2	1	no	—
141	C₄×#168	C₂³	1	1	yes	characteristic
142	C₄×#168	C₂³	1	1	yes	characteristic
143	C₄×#168	C₂³	1	1	yes	characteristic
144	C₄×#168	C₂³	1	1	yes	characteristic
145	#3102	—	5	1	no	—
146	#2971	D₅	1	1	yes	characteristic, complemented
147	#2969	—	5	1	no	—
148	#1594	—	5	1	no	—
149	#1592	—	5	1	no	—
150	#1588	—	5	1	no	—
151	#1588	—	5	1	no	—
152	#1587	—	5	1	no	—
153	#1586	—	5	1	no	—
154	#1579	—	5	1	no	—
155	SD₁₆⋊C₈	—	5	1	no	—
156	#1572	—	5	1	no	—
157	#1494	—	5	1	no	—
158	#1476	—	5	1	no	—
159	#1451	—	5	1	no	—
160	C₅×#41	—	2	2	no	—
161	C₅×#41	—	4	1	no	—
162	C₂×C₅×Q₈	C₂²×C₄	1	1	yes	characteristic
163	C₂×C₅×D₄	—	2	1	no	—
164	C₂×C₅×D₄	C₂²×C₄	1	1	yes	characteristic
165	C₂²×C₄×C₅	—	2	1	no	—
166	C₂²×C₄×C₅	—	2	1	no	—
167	C₂²×C₄×C₅	—	2	1	no	—
168	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
169	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
170	C₂²×C₄×C₅	#41	1	1	yes	characteristic
171	C₂×C₂²⋊D₅	—	2	1	no	—
172	C₂×D₂₀	C₂²×C₄	1	1	yes	characteristic
173	C₂×C₄×D₅	—	2	1	no	—
174	C₂×Dic₁₀	C₂²×C₄	1	1	yes	characteristic
175	C₅×M₁₆	—	4	1	no	—
176	C₅×M₁₆	—	4	1	no	—
177	C₅×M₁₆	—	4	2	no	—
178	C₅×M₁₆	—	4	2	no	—
179	C₂×C₅×C₈	—	2	1	no	—
180	C₂×C₅×C₈	—	2	1	no	—
181	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
182	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
183	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
184	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
185	C₅×C₄⋊C₄	—	2	1	no	—
186	C₅×C₄⋊C₄	—	2	1	no	—
187	C₅×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
188	C₅×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
189	C₅×C₂²⋊C₄	—	2	1	no	—
190	C₅×C₂²⋊C₄	—	2	1	no	—
191	C₅×C₂²⋊C₄	—	2	1	no	—
192	C₄²×C₅	—	2	1	no	—
193	C₄²×C₅	—	2	1	no	—
194	C₄²×C₅	—	2	1	no	—
195	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
196	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
197	C₄²×C₅	#41	1	1	yes	characteristic
198	C₄²×C₅	C₂⁴	1	1	yes	characteristic
199	C₂²⋊Dic₅	—	2	1	no	—
200	#689	—	2	2	no	—
201	#688	—	2	2	no	—
202	#687	—	4	1	no	—
203	#686	—	4	1	no	—
204	#685	—	2	1	no	—
205	#685	—	2	1	no	—
206	#685	—	2	1	no	—
207	#685	—	2	1	no	—
208	C₄⋊Dic₅	C₂²×C₄	1	1	yes	characteristic
209	C₄⋊Dic₅	C₂²×C₄	1	1	yes	characteristic
210	#683	—	2	1	no	—
211	#683	—	2	1	no	—
212	#683	—	2	1	no	—
213	#683	—	2	1	no	—
214	C₄×Dic₅	—	2	1	no	—
215	C₂×#168	—	2	1	no	—
216	C₂×#168	—	2	1	no	—
217	C₂×#168	—	2	1	no	—
218	C₂×#168	—	2	1	no	—
219	C₂×#168	—	4	2	no	—
220	C₂×#168	C₂²×C₄	1	1	yes	characteristic
221	C₂×#168	C₂²×C₄	1	1	yes	characteristic
222	C₂×#168	C₂²×C₄	1	1	yes	characteristic
223	C₂×#168	C₂²×C₄	1	1	yes	characteristic
224	#676	—	4	2	no	—
225	C₈×D₅	—	4	2	no	—
226	#529	—	5	1	no	—
227	C₄×#41	C₂×D₅	1	1	yes	characteristic
228	#485	—	5	1	no	—
229	#482	—	5	1	no	—
230	#479	—	5	1	no	—
231	#478	—	5	1	no	—
232	#464	—	5	1	no	—
233	#463	—	5	1	no	—
234	#452	—	5	1	no	—
235	#449	—	5	1	no	—
236	#446	—	5	1	no	—
237	C₈×Q₈	—	5	1	no	—
238	C₈×Q₈	C₂×D₅	1	1	yes	characteristic
239	C₈×Q₈	C₂×D₅	1	1	yes	characteristic
240	C₄×Q₁₆	—	5	1	no	—
241	C₄×SD₁₆	—	5	1	no	—
242	C₄×SD₁₆	—	5	1	no	—
243	C₄×D₈	—	5	1	no	—
244	#436	—	2	1	no	—
245	#436	—	2	1	no	—
246	#436	—	5	1	no	—
247	#436	—	10	1	no	—
248	#436	C₂×D₅	1	1	yes	characteristic
249	#436	C₂×D₅	1	1	yes	characteristic
250	#435	—	10	1	no	—
251	C₈×D₄	—	5	1	no	—
252	#433	—	10	1	no	—
253	#432	—	2	1	no	—
254	#432	C₂×D₅	1	1	yes	characteristic
255	#431	—	5	1	no	—
256	#431	—	5	1	no	—
257	#405	—	10	1	no	—
258	C₄×M₁₆	—	2	1	no	—
259	C₄×M₁₆	C₂×D₅	1	1	yes	characteristic
260	C₂×C₄×C₈	—	5	1	no	—
261	#335	—	5	1	no	—
262	#335	—	5	1	no	—
263	#334	—	5	1	no	—
264	#334	—	5	1	no	—
265	Q₈⋊C₈	—	5	1	no	—
266	Q₈⋊C₈	—	5	1	no	—
267	Q₈⋊C₈	—	5	1	no	—
268	Q₈⋊C₈	—	5	1	no	—
269	D₄⋊C₈	—	5	1	no	—
270	D₄⋊C₈	—	5	1	no	—
271	D₄⋊C₈	—	5	1	no	—
272	D₄⋊C₈	—	5	1	no	—
273	#322	—	5	1	no	—
274	#322	—	5	1	no	—
275	#322	—	5	1	no	—
276	#322	—	5	1	no	—
277	C₂³×C₅	—	2	1	no	—
278	C₂³×C₅	C₄×D₄	1	1	yes	characteristic
279	C₂²×D₅	—	2	1	no	—
280	C₅×Q₈	—	2	1	no	—
281	C₅×Q₈	#131	1	2	yes	—
282	C₅×D₄	—	2	1	no	—
283	C₅×D₄	—	2	1	no	—
284	C₅×D₄	—	4	2	no	—
285	C₂×C₄×C₅	—	2	1	no	—
286	C₂×C₄×C₅	—	2	1	no	—
287	C₂×C₄×C₅	—	2	1	no	—
288	C₂×C₄×C₅	—	2	1	no	—
289	C₂×C₄×C₅	—	2	1	no	—
290	C₂×C₄×C₅	—	2	1	no	—
291	C₂×C₄×C₅	—	2	1	no	—
292	C₂×C₄×C₅	—	4	1	no	—
293	C₂×C₄×C₅	—	4	2	no	—
294	C₂×C₄×C₅	—	4	1	no	—
295	C₂×C₄×C₅	—	4	1	no	—
296	C₂×C₄×C₅	—	8	1	no	—
297	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
298	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
299	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
300	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
301	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
302	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
303	C₂²⋊D₅	—	8	1	no	—
304	C₂×Dic₅	—	2	1	no	—
305	C₂×Dic₅	—	2	1	no	—
306	C₂×Dic₅	—	2	1	no	—
307	D₂₀	—	2	1	no	—
308	D₂₀	—	2	1	no	—
309	C₄×D₅	—	4	1	no	—
310	C₄×D₅	—	4	1	no	—
311	Dic₁₀	—	2	1	no	—
312	Dic₁₀	—	2	1	no	—
313	C₅×C₈	—	2	1	no	—
314	C₅×C₈	—	2	1	no	—
315	C₅×C₈	—	2	1	no	—
316	C₅×C₈	—	2	1	no	—
317	C₅×C₈	—	4	1	no	—
318	C₅×C₈	—	4	1	no	—
319	#168	—	2	2	no	—
320	#168	—	2	1	no	—
321	#168	—	2	1	no	—
322	#168	—	2	1	no	—
323	#168	—	2	1	no	—
324	#168	—	4	1	no	—
325	#168	—	4	1	no	—
326	#168	—	4	1	no	—
327	C₂×#41	C₄×D₅	1	1	yes	characteristic
328	C₂×Q₁₆	—	5	1	no	—
329	C₂×SD₁₆	—	5	1	no	—
330	C₂×SD₁₆	—	5	1	no	—
331	C₂×D₈	—	5	1	no	—
332	C₂×M₁₆	—	2	1	no	—
333	C₂×M₁₆	—	2	1	no	—
334	C₂×M₁₆	—	10	1	no	—
335	C₂×M₁₆	C₂²⋊D₅	1	1	yes	characteristic
336	C₂×M₁₆	C₂²⋊D₅	1	1	yes	characteristic
337	C₂²×C₈	—	10	1	no	—
338	C₂²×C₈	—	10	1	no	—
339	#126	—	10	1	no	—
340	#125	—	5	1	no	—
341	#124	—	5	1	no	—
342	#123	—	10	1	no	—
343	C₂²⋊Q₈	—	5	1	no	—
344	#121	—	5	1	no	—
345	C₄×Q₈	—	5	1	no	—
346	C₄×Q₈	C₄×D₅	1	1	yes	characteristic
347	C₄×Q₈	C₂²×D₅	1	1	yes	characteristic
348	C₄×D₄	—	2	1	no	—
349	C₄×D₄	—	2	1	no	—
350	C₄×D₄	—	5	1	no	—
351	C₄×D₄	—	10	1	no	—
352	C₄×D₄	C₄×D₅	1	1	yes	characteristic
353	C₄×D₄	C₂²×D₅	1	1	yes	characteristic
354	#117	—	2	1	no	—
355	#117	—	10	1	no	—
356	#117	C₄×D₅	1	1	yes	characteristic
357	C₂×C₄²	—	2	1	no	—
358	C₂×C₄²	C₂²×D₅	1	1	yes	characteristic
359	#107	—	5	1	no	—
360	#107	—	5	1	no	—
361	#106	—	5	1	no	—
362	#106	—	5	1	no	—
363	C₄⋊C₈	—	2	1	no	—
364	C₄⋊C₈	—	2	1	no	—
365	C₄⋊C₈	—	5	1	no	—
366	C₄⋊C₈	—	5	1	no	—
367	C₄⋊C₈	—	5	1	no	—
368	C₄⋊C₈	—	5	1	no	—
369	C₄⋊C₈	—	10	1	no	—
370	C₄⋊C₈	—	10	1	no	—
371	C₄⋊C₈	C₂²×D₅	1	1	yes	characteristic
372	C₄⋊C₈	C₂²×D₅	1	1	yes	characteristic
373	#103	—	5	1	no	—
374	#103	—	5	1	no	—
375	#103	—	5	1	no	—
376	#103	—	5	1	no	—
377	#102	—	5	1	no	—
378	#102	—	5	1	no	—
379	#102	—	5	1	no	—
380	#102	—	5	1	no	—
381	C₂²⋊C₈	—	2	1	no	—
382	C₂²⋊C₈	—	2	1	no	—
383	C₂²⋊C₈	—	2	1	no	—
384	C₂²⋊C₈	—	5	1	no	—
385	C₂²⋊C₈	—	5	1	no	—
386	C₂²⋊C₈	—	10	1	no	—
387	C₂²⋊C₈	—	10	1	no	—
388	C₂²⋊C₈	—	10	1	no	—
389	#97	—	2	1	no	—
390	#97	—	10	1	no	—
391	#97	C₂²⋊D₅	1	1	yes	characteristic
392	#97	C₂²⋊D₅	1	1	yes	characteristic
393	C₄×C₈	—	2	1	no	—
394	C₄×C₈	—	2	1	no	—
395	C₄×C₈	—	5	1	no	—
396	C₄×C₈	—	5	1	no	—
397	C₄×C₈	—	5	1	no	—
398	C₄×C₈	—	5	1	no	—
399	C₄×C₈	—	10	1	no	—
400	C₄×C₈	—	10	1	no	—
401	C₄×C₈	—	10	1	no	—
402	C₄×C₈	C₂²×D₅	1	1	yes	characteristic
403	C₄×C₈	C₂²×D₅	1	1	yes	characteristic
404	C₂²×C₅	—	2	1	no	—
405	C₂²×C₅	—	2	1	no	—
406	C₂²×C₅	—	2	1	no	—
407	C₂²×C₅	—	4	1	no	—
408	C₂²×C₅	—	4	1	no	—
409	C₂²×C₅	—	4	1	no	—
410	C₂²×C₅	C₂×C₄×D₄	1	1	yes	characteristic
411	C₂×D₅	—	4	1	no	—
412	C₂×D₅	—	4	1	no	—
413	C₂×D₅	—	4	1	no	—
414	C₄×C₅	—	2	1	no	—
415	C₄×C₅	—	2	2	no	—
416	C₄×C₅	—	2	1	no	—
417	C₄×C₅	—	2	1	no	—
418	C₄×C₅	—	2	1	no	—
419	C₄×C₅	—	4	1	no	—
420	C₄×C₅	—	4	1	no	—
421	C₄×C₅	C₂×#131	1	1	yes	characteristic
422	C₄×C₅	#568	1	1	yes	characteristic
423	C₄×C₅	#575	1	1	yes	characteristic
424	C₄×C₅	#575	1	1	yes	characteristic
425	Dic₅	—	4	1	no	—
426	Dic₅	—	4	1	no	—
427	Dic₅	—	4	1	no	—
428	#41	—	2	2	no	—
429	#41	—	4	1	no	—
430	C₂×Q₈	—	5	1	no	—
431	C₂×Q₈	C₂×C₄×D₅	1	1	yes	characteristic
432	C₂×D₄	—	2	1	no	—
433	C₂×D₄	—	5	1	no	—
434	C₂×D₄	—	10	1	no	—
435	C₂×D₄	C₂×C₄×D₅	1	1	yes	characteristic
436	C₂²×C₄	—	2	1	no	—
437	C₂²×C₄	—	2	1	no	—
438	C₂²×C₄	—	2	1	no	—
439	C₂²×C₄	—	10	1	no	—
440	C₂²×C₄	C₂×C₄×D₅	1	1	yes	characteristic
441	C₂²×C₄	#709	1	1	yes	characteristic
442	C₂²×C₄	C₂×C₂²⋊D₅	1	1	yes	characteristic
443	Q₁₆	—	10	2	no	—
444	SD₁₆	—	10	2	no	—
445	SD₁₆	—	20	1	no	—
446	D₈	—	20	1	no	—
447	M₁₆	—	4	1	no	—
448	M₁₆	—	4	1	no	—
449	M₁₆	—	4	2	no	—
450	M₁₆	—	4	2	no	—
451	M₁₆	—	20	2	no	—
452	C₂×C₈	—	2	1	no	—
453	C₂×C₈	—	2	1	no	—
454	C₂×C₈	—	5	1	no	—
455	C₂×C₈	—	5	1	no	—
456	C₂×C₈	—	5	1	no	—
457	C₂×C₈	—	5	1	no	—
458	C₂×C₈	—	10	1	no	—
459	C₂×C₈	—	10	1	no	—
460	C₂×C₈	—	10	1	no	—
461	C₂×C₈	—	10	1	no	—
462	C₂×C₈	—	20	2	no	—
463	C₂×C₈	—	20	2	no	—
464	C₂×C₈	C₂×C₂²⋊D₅	1	1	yes	characteristic
465	C₂×C₈	C₂×C₂²⋊D₅	1	1	yes	characteristic
466	C₂×C₈	C₂×C₂²⋊D₅	1	1	yes	characteristic
467	C₂×C₈	C₂×C₂²⋊D₅	1	1	yes	characteristic
468	C₄⋊C₄	—	2	1	no	—
469	C₄⋊C₄	—	2	1	no	—
470	C₄⋊C₄	—	5	1	no	—
471	C₄⋊C₄	—	5	1	no	—
472	C₄⋊C₄	—	10	1	no	—
473	C₄⋊C₄	—	10	1	no	—
474	C₄⋊C₄	—	10	1	no	—
475	C₄⋊C₄	—	10	1	no	—
476	C₄⋊C₄	C₂×C₄×D₅	1	1	yes	characteristic
477	C₄⋊C₄	C₂×C₄×D₅	1	1	yes	characteristic
478	C₂²⋊C₄	—	2	1	no	—
479	C₂²⋊C₄	—	2	1	no	—
480	C₂²⋊C₄	—	2	1	no	—
481	C₂²⋊C₄	—	10	1	no	—
482	C₂²⋊C₄	—	10	1	no	—
483	C₂²⋊C₄	—	10	1	no	—
484	C₂²⋊C₄	—	10	1	no	—
485	C₂²⋊C₄	—	10	1	no	—
486	C₄²	—	2	1	no	—
487	C₄²	—	2	1	no	—
488	C₄²	—	2	1	no	—
489	C₄²	—	10	1	no	—
490	C₄²	C₂×C₄×D₅	1	1	yes	characteristic
491	C₄²	#709	1	1	yes	characteristic
492	C₄²	C₂×C₂²⋊D₅	1	1	yes	characteristic
493	C₄²	C₂³×D₅	1	1	yes	characteristic
494	C₂×C₅	—	4	1	no	—
495	C₂×C₅	—	8	1	no	—
496	C₂×C₅	#2933	1	1	yes	characteristic
497	C₂×C₅	#2943	1	1	yes	characteristic
498	C₂×C₅	#2956	1	1	yes	characteristic
499	D₅	—	8	1	no	—
500	C₂³	—	2	1	no	—
501	C₂³	—	10	1	no	—
502	C₂³	C₄×C₂²⋊D₅	1	1	yes	characteristic
503	Q₈	—	2	1	no	—
504	Q₈	—	10	1	no	—
505	Q₈	—	10	1	no	—
506	Q₈	#4053	1	2	yes	—
507	D₄	—	2	1	no	—
508	D₄	—	2	1	no	—
509	D₄	—	4	2	no	—
510	D₄	—	10	1	no	—
511	D₄	—	10	1	no	—
512	D₄	—	40	1	no	—
513	C₂×C₄	—	2	1	no	—
514	C₂×C₄	—	2	1	no	—
515	C₂×C₄	—	2	1	no	—
516	C₂×C₄	—	2	1	no	—
517	C₂×C₄	—	2	1	no	—
518	C₂×C₄	—	2	1	no	—
519	C₂×C₄	—	2	1	no	—
520	C₂×C₄	—	4	1	no	—
521	C₂×C₄	—	4	2	no	—
522	C₂×C₄	—	4	1	no	—
523	C₂×C₄	—	4	1	no	—
524	C₂×C₄	—	8	1	no	—
525	C₂×C₄	—	10	1	no	—
526	C₂×C₄	—	10	1	no	—
527	C₂×C₄	—	10	1	no	—
528	C₂×C₄	—	20	1	no	—
529	C₂×C₄	—	20	1	no	—
530	C₂×C₄	C₄×C₂²⋊D₅	1	1	yes	characteristic
531	C₂×C₄	C₄×C₂²⋊D₅	1	1	yes	characteristic
532	C₂×C₄	C₄×C₂²⋊D₅	1	1	yes	characteristic
533	C₂×C₄	C₂²×C₄×D₅	1	1	yes	characteristic
534	C₂×C₄	C₂×#709	1	1	yes	characteristic
535	C₂×C₄	C₂²×C₂²⋊D₅	1	1	yes	characteristic
536	C₈	—	2	1	no	—
537	C₈	—	2	1	no	—
538	C₈	—	2	1	no	—
539	C₈	—	2	1	no	—
540	C₈	—	4	1	no	—
541	C₈	—	4	1	no	—
542	C₈	—	10	2	no	—
543	C₈	—	10	1	no	—
544	C₈	—	10	1	no	—
545	C₈	—	10	1	no	—
546	C₈	—	10	1	no	—
547	C₈	—	20	1	no	—
548	C₈	—	20	1	no	—
549	C₈	—	20	1	no	—
550	C₅	#18005	1	1	yes	characteristic, complemented, Sylow
551	C₂²	—	2	1	no	—
552	C₂²	—	2	1	no	—
553	C₂²	—	2	1	no	—
554	C₂²	—	4	1	no	—
555	C₂²	—	4	1	no	—
556	C₂²	—	4	1	no	—
557	C₂²	—	20	1	no	—
558	C₂²	—	20	1	no	—
559	C₂²	—	20	1	no	—
560	C₂²	C₂×C₄×C₂²⋊D₅	1	1	yes	characteristic
561	C₄	—	2	1	no	—
562	C₄	—	2	2	no	—
563	C₄	—	2	1	no	—
564	C₄	—	2	1	no	—
565	C₄	—	2	1	no	—
566	C₄	—	4	1	no	—
567	C₄	—	4	1	no	—
568	C₄	—	20	1	no	—
569	C₄	—	20	1	no	—
570	C₄	—	20	1	no	—
571	C₄	C₂×#4053	1	1	yes	characteristic
572	C₄	#66079	1	1	yes	characteristic
573	C₄	#66156	1	1	yes	characteristic
574	C₄	#66156	1	1	yes	characteristic
575	C₂	—	4	1	no	—
576	C₂	—	8	1	no	—
577	C₂	—	40	1	no	—
578	C₂	#10614237	1	1	yes	characteristic
579	C₂	#10615488	1	1	yes	characteristic
580	C₂	#10615542	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×C₂²⋊D₅
commutator	C₂×C₄×C₅	C₂³×C₄
Frattini	C₄²	C₂³×D₅
Fitting	C₅×#2971	C₂
socle	C₂²×C₅	C₂×C₄×D₄
prime radical	#65527	C₄
cosocle	C₄²×C₅	C₂⁴
hypercenter	#2971	D₅
hypocenter	C₅	#18005
LCS	G ▷ C₂×C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₄ ◁ C₄×M₁₆ ◁ #2971

Complements

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

N	H ≅ G/N	type
1. C₅×#2971	C₂	semidirect
3. #10610242	C₂	semidirect
4. #10602431	C₂	semidirect
5. #10601730	C₂	semidirect
6. #10601729	C₂	semidirect
7. #10601728	C₂	semidirect
8. #10601725	C₂	semidirect
9. #10601658	C₂	semidirect
10. #10601656	C₂	semidirect
11. #10601654	C₂	semidirect
12. #10601653	C₂	semidirect
13. #10601593	C₂	semidirect
14. #10601589	C₂	semidirect
15. #10600640	C₂	semidirect
146. #2971	D₅	semidirect
550. C₅	#18005	semidirect

Maximal subgroups

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

subgroup	index
C₅×#2971	2
#10614259	2
#10610242	2
#10602431	2
#10601730	2
#10601729	2
#10601728	2
#10601725	2
#10601658	2
#10601656	2
#10601654	2
#10601653	2
#10601593	2
#10601589	2
#10600640	2
#18005	5