Subgroups — #12069366

Order 1280.

648 conjugacy classes of subgroups.

The subgroup lattice has 606 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#10614872	C₂	1	1	yes	maximal, characteristic
2	#10614862	C₂	1	1	yes	maximal, characteristic, complemented
3	#10611017	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#1482	C₂	1	1	yes	maximal, characteristic, complemented
5	#10601555	C₂	1	1	yes	maximal, characteristic, complemented
6	#10601541	C₂	1	1	yes	maximal, characteristic, complemented
7	#10601537	C₂	1	1	yes	maximal, characteristic, complemented
8	#10599013	C₂	1	1	yes	maximal, characteristic, complemented
9	#10599009	C₂	1	1	yes	maximal, characteristic, complemented
10	#10599007	C₂	1	1	yes	maximal, characteristic, complemented
11	#10599005	C₂	1	1	yes	maximal, characteristic, complemented
12	#10598951	C₂	1	1	yes	maximal, characteristic, complemented
13	#10598946	C₂	1	1	yes	maximal, characteristic, complemented
14	#10598944	C₂	1	1	yes	maximal, characteristic, complemented
15	#10598941	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅×#529	C₂²	1	1	yes	characteristic
17	C₂×C₄×D₂₀	C₂²	1	1	yes	characteristic
18	C₅×#431	C₂²	1	1	yes	characteristic
19	C₅×#431	C₂²	1	1	yes	characteristic
20	#65355	C₄	1	1	yes	characteristic
21	#65355	C₄	1	1	yes	characteristic
22	#65346	C₄	1	1	yes	characteristic
23	#65346	C₄	1	1	yes	characteristic
24	#65335	C₄	1	1	yes	characteristic
25	#65333	C₄	1	1	yes	characteristic
26	#65325	C₄	1	1	yes	characteristic
27	#65323	C₄	1	1	yes	characteristic
28	C₄×#688	C₂²	1	1	yes	characteristic
29	C₄×#688	C₂²	1	1	yes	characteristic
30	#65313	C₂²	1	1	yes	characteristic, complemented
31	Q₈×#168	C₂²	1	1	yes	characteristic, complemented
32	C₄×#686	C₂²	1	1	yes	characteristic
33	C₄×#686	C₂²	1	1	yes	characteristic
34	#65301	—	2	1	no	—
35	#65301	C₂²	1	1	yes	characteristic, complemented
36	#65300	—	2	1	no	—
37	D₄×#168	C₂²	1	1	yes	characteristic, complemented
38	#65289	—	2	1	no	—
39	#65288	—	2	1	no	—
40	#65214	C₂²	1	1	yes	characteristic
41	#65214	C₂²	1	1	yes	characteristic
42	#65213	C₂²	1	1	yes	characteristic
43	#65123	C₂²	1	1	yes	characteristic
44	#65123	C₂²	1	1	yes	characteristic
45	#65123	C₂²	1	1	yes	characteristic
46	#65123	C₂²	1	1	yes	characteristic
47	D₅×C₂²⋊C₈	—	2	1	no	—
48	D₅×C₂²⋊C₈	—	2	1	no	—
49	C₈×D₂₀	—	2	1	no	—
50	C₈×D₂₀	—	2	1	no	—
51	C₅×Q₈⋊C₈	C₂²	1	1	yes	characteristic, complemented
52	C₅×Q₈⋊C₈	C₂²	1	1	yes	characteristic, complemented
53	C₅×D₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
54	C₅×D₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
55	#64700	C₂²	1	1	yes	characteristic, complemented
56	#64700	C₂²	1	1	yes	characteristic, complemented
57	#64699	C₂²	1	1	yes	characteristic, complemented
58	#64699	C₂²	1	1	yes	characteristic, complemented
59	#64679	C₂²	1	1	yes	characteristic
60	#64679	C₂²	1	1	yes	characteristic
61	#64679	C₂²	1	1	yes	characteristic
62	#64679	C₂²	1	1	yes	characteristic
63	#64675	C₂²	1	1	yes	characteristic, complemented
64	#64674	C₂²	1	1	yes	characteristic, complemented
65	#64674	C₂²	1	1	yes	characteristic, complemented
66	C₈×#168	C₂²	1	1	yes	characteristic, complemented
67	#17918	—	5	1	no	maximal, Sylow
68	C₂²×D₂₀	C₂×C₄	1	1	yes	characteristic
69	C₂²×C₄×D₅	—	2	1	no	—
70	C₅×#126	—	2	1	no	—
71	C₅×#125	C₂×C₄	1	1	yes	characteristic
72	C₅×#124	C₂×C₄	1	1	yes	characteristic
73	C₅×#123	—	2	1	no	—
74	C₅×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
75	C₅×#121	C₂×C₄	1	1	yes	characteristic
76	C₄×C₅×Q₈	C₂³	1	1	yes	characteristic
77	C₄×C₅×D₄	—	2	1	no	—
78	C₄×C₅×D₄	C₂³	1	1	yes	characteristic
79	C₅×#117	—	2	1	no	—
80	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
81	C₂×#688	C₂×C₄	1	1	yes	characteristic
82	C₂×#688	C₂×C₄	1	1	yes	characteristic
83	C₂×#686	C₂×C₄	1	1	yes	characteristic
84	C₂×#686	C₂×C₄	1	1	yes	characteristic
85	C₂×#685	—	2	1	no	—
86	C₂×C₄⋊Dic₅	C₂×C₄	1	1	yes	characteristic
87	C₂×#681	—	2	1	no	—
88	C₂×#681	—	2	1	no	—
89	C₂²×#168	—	2	1	no	—
90	C₂×C₈×D₅	—	2	1	no	—
91	C₂×C₈×D₅	—	2	1	no	—
92	C₂×C₈×D₅	—	2	1	no	—
93	C₂×C₈×D₅	—	2	1	no	—
94	C₄×D₂₀	—	2	1	no	—
95	C₄×D₂₀	—	2	1	no	—
96	C₄×D₂₀	C₂×C₄	1	1	yes	characteristic
97	C₄×D₂₀	C₂×C₄	1	1	yes	characteristic
98	C₄×D₂₀	C₂³	1	1	yes	characteristic
99	C₄×D₂₀	C₂³	1	1	yes	characteristic
100	C₅×C₄⋊C₈	—	2	1	no	—
101	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
102	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
103	C₅×C₂²⋊C₈	—	2	1	no	—
104	C₅×C₂²⋊C₈	—	2	1	no	—
105	C₄×C₅×C₈	—	2	1	no	—
106	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
107	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
108	#3967	C₂×C₄	1	1	yes	characteristic
109	#3967	C₂×C₄	1	1	yes	characteristic
110	#3964	C₂×C₄	1	1	yes	characteristic
111	#3964	C₂×C₄	1	1	yes	characteristic
112	C₂²⋊#168	—	2	1	no	—
113	C₂²⋊#168	—	2	1	no	—
114	C₂²⋊#168	C₂×C₄	1	1	yes	characteristic
115	C₂²⋊#168	C₂×C₄	1	1	yes	characteristic
116	C₂²⋊#168	D₄	1	1	yes	characteristic
117	C₂²⋊#168	D₄	1	1	yes	characteristic
118	#3952	—	2	1	no	—
119	#3952	—	2	1	no	—
120	#3952	—	2	1	no	—
121	#3952	—	2	1	no	—
122	#3941	C₂×C₄	1	1	yes	characteristic
123	#3941	C₂×C₄	1	1	yes	characteristic
124	#3941	C₂×C₄	1	1	yes	characteristic
125	#3941	C₂×C₄	1	1	yes	characteristic
126	#3940	C₂×C₄	1	1	yes	characteristic
127	#3940	C₂×C₄	1	1	yes	characteristic
128	#3939	C₂×C₄	1	1	yes	characteristic
129	#3939	C₂×C₄	1	1	yes	characteristic
130	C₄⋊#168	—	2	1	no	—
131	C₄⋊#168	—	2	1	no	—
132	C₄⋊#168	—	2	1	no	—
133	C₄⋊#168	C₂×C₄	1	1	yes	characteristic
134	C₄⋊#168	C₂×C₄	1	1	yes	characteristic
135	C₄⋊#168	D₄	1	1	yes	characteristic
136	C₄⋊#168	D₄	1	1	yes	characteristic
137	C₄⋊#168	C₂³	1	1	yes	characteristic
138	C₄⋊#168	C₂³	1	1	yes	characteristic
139	#3935	—	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	#3105	—	5	1	no	—
146	#2993	—	5	1	no	—
147	#2972	—	5	1	no	—
148	#1586	—	5	1	no	—
149	#1585	—	5	1	no	—
150	#1582	—	5	1	no	—
151	#1581	—	5	1	no	—
152	#1580	—	5	1	no	—
153	SD₁₆⋊C₈	—	5	1	no	—
154	C₈×SD₁₆	—	5	1	no	—
155	C₈×D₈	—	5	1	no	—
156	#1574	—	5	1	no	—
157	#1486	—	5	1	no	—
158	#1482	D₅	1	1	yes	characteristic, complemented
159	#1454	—	5	1	no	—
160	C₂³×D₅	—	2	1	no	—
161	C₂×C₅×Q₈	C₂²×C₄	1	1	yes	characteristic
162	C₂×C₅×D₄	—	2	1	no	—
163	C₂×C₅×D₄	C₂²×C₄	1	1	yes	characteristic
164	C₂²×C₄×C₅	—	2	1	no	—
165	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
166	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
167	C₂²×C₄×C₅	#41	1	1	yes	characteristic
168	C₂²×Dic₅	—	2	1	no	—
169	C₂×D₂₀	—	2	1	no	—
170	C₂×D₂₀	—	2	2	no	—
171	C₂×D₂₀	—	2	2	no	—
172	C₂×D₂₀	C₂²×C₄	1	1	yes	characteristic
173	C₂×D₂₀	C₂²×C₄	1	1	yes	characteristic
174	C₂×C₄×D₅	—	2	1	no	—
175	C₂×C₄×D₅	—	2	1	no	—
176	C₂×C₄×D₅	—	2	1	no	—
177	C₂×C₄×D₅	—	2	1	no	—
178	C₂×C₄×D₅	—	8	1	no	—
179	C₂×C₄×D₅	—	8	1	no	—
180	C₂×C₅×C₈	—	2	1	no	—
181	C₂×C₅×C₈	—	2	1	no	—
182	C₂×C₅×C₈	—	2	1	no	—
183	C₂×C₅×C₈	—	2	1	no	—
184	C₅×C₄⋊C₄	—	2	1	no	—
185	C₅×C₄⋊C₄	—	2	1	no	—
186	C₅×C₄⋊C₄	—	2	1	no	—
187	C₅×C₄⋊C₄	—	2	1	no	—
188	C₅×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
189	C₅×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
190	C₅×C₂²⋊C₄	—	2	1	no	—
191	C₅×C₂²⋊C₄	—	2	1	no	—
192	C₅×C₂²⋊C₄	—	2	1	no	—
193	C₅×C₂²⋊C₄	—	2	1	no	—
194	C₅×C₂²⋊C₄	—	2	1	no	—
195	C₄²×C₅	—	2	1	no	—
196	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
197	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
198	C₄²×C₅	#41	1	1	yes	characteristic
199	C₄²×C₅	C₂⁴	1	1	yes	characteristic
200	#688	—	2	2	no	—
201	#688	—	2	2	no	—
202	#686	—	2	2	no	—
203	#686	—	2	2	no	—
204	#685	—	2	1	no	—
205	#685	—	2	1	no	—
206	#685	—	2	1	no	—
207	#685	—	2	1	no	—
208	C₄⋊Dic₅	—	2	1	no	—
209	C₄⋊Dic₅	C₂²×C₄	1	1	yes	characteristic
210	C₄⋊Dic₅	C₂²×C₄	1	1	yes	characteristic
211	#681	—	8	1	no	—
212	#681	—	8	1	no	—
213	C₂×#168	—	2	1	no	—
214	C₂×#168	—	2	1	no	—
215	C₂×#168	—	8	1	no	—
216	C₂×#168	C₂²×C₄	1	1	yes	characteristic
217	C₂×#168	C₂²×C₄	1	1	yes	characteristic
218	C₂×#168	C₂²×C₄	1	1	yes	characteristic
219	C₂×#168	C₂²×C₄	1	1	yes	characteristic
220	C₂×#168	C₂×D₄	1	1	yes	characteristic
221	C₂×#168	C₂×D₄	1	1	yes	characteristic
222	C₂×#168	C₂×D₄	1	1	yes	characteristic
223	C₂×#168	C₂×D₄	1	1	yes	characteristic
224	C₈×D₅	—	8	1	no	—
225	C₈×D₅	—	8	1	no	—
226	C₈×D₅	—	8	1	no	—
227	C₈×D₅	—	8	1	no	—
228	#529	C₂×D₅	1	1	yes	characteristic
229	C₂×C₄×D₄	—	5	1	no	—
230	#484	—	5	1	no	—
231	#481	—	5	1	no	—
232	#478	—	5	1	no	—
233	#478	—	5	1	no	—
234	#463	—	5	1	no	—
235	#463	—	5	1	no	—
236	#450	—	5	1	no	—
237	#447	—	5	1	no	—
238	#446	—	5	1	no	—
239	C₈×Q₈	—	5	1	no	—
240	C₄×SD₁₆	—	5	1	no	—
241	C₄×SD₁₆	—	5	1	no	—
242	C₄×D₈	—	5	1	no	—
243	C₄×D₈	—	5	1	no	—
244	#436	—	5	1	no	—
245	#436	—	10	1	no	—
246	#435	—	10	1	no	—
247	C₈×D₄	—	5	1	no	—
248	C₈×D₄	—	5	1	no	—
249	C₈×D₄	—	5	1	no	—
250	C₈×D₄	—	5	1	no	—
251	C₈×D₄	—	5	1	no	—
252	C₈×D₄	—	10	1	no	—
253	C₈×D₄	—	10	1	no	—
254	#433	—	10	1	no	—
255	#431	—	5	1	no	—
256	#431	—	5	1	no	—
257	#431	C₂×D₅	1	1	yes	characteristic
258	#431	C₂×D₅	1	1	yes	characteristic
259	#424	—	10	1	no	—
260	#423	—	5	1	no	—
261	C₂×C₂²⋊C₈	—	10	1	no	—
262	C₂×C₂²⋊C₈	—	10	1	no	—
263	#335	—	5	1	no	—
264	#335	—	5	1	no	—
265	#334	—	5	1	no	—
266	#334	—	5	1	no	—
267	Q₈⋊C₈	C₂×D₅	1	1	yes	characteristic, complemented
268	Q₈⋊C₈	C₂×D₅	1	1	yes	characteristic, complemented
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	D₄⋊C₈	C₂×D₅	1	1	yes	characteristic, complemented
274	D₄⋊C₈	C₂×D₅	1	1	yes	characteristic, complemented
275	#322	—	5	1	no	—
276	#322	—	5	1	no	—
277	#322	—	5	1	no	—
278	C₈²	—	5	1	no	—
279	C₂³×C₅	—	2	1	no	—
280	C₂³×C₅	C₄×D₄	1	1	yes	characteristic
281	C₂²×D₅	—	2	1	no	—
282	C₂²×D₅	—	2	1	no	—
283	C₂²×D₅	—	2	4	no	—
284	C₂²×D₅	—	8	1	no	—
285	C₂²×D₅	—	8	1	no	—
286	C₅×Q₈	—	2	1	no	—
287	C₅×Q₈	—	2	1	no	—
288	C₅×D₄	—	2	1	no	—
289	C₅×D₄	—	2	1	no	—
290	C₅×D₄	—	8	1	no	—
291	C₂×C₄×C₅	—	2	1	no	—
292	C₂×C₄×C₅	—	2	1	no	—
293	C₂×C₄×C₅	—	2	1	no	—
294	C₂×C₄×C₅	—	2	1	no	—
295	C₂×C₄×C₅	—	2	1	no	—
296	C₂×C₄×C₅	—	2	1	no	—
297	C₂×C₄×C₅	—	2	1	no	—
298	C₂×C₄×C₅	—	4	1	no	—
299	C₂×C₄×C₅	—	4	1	no	—
300	C₂×C₄×C₅	—	4	1	no	—
301	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
302	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
303	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
304	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
305	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
306	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
307	C₂×Dic₅	—	2	1	no	—
308	C₂×Dic₅	—	2	1	no	—
309	C₂×Dic₅	—	8	1	no	—
310	D₂₀	—	2	4	no	—
311	D₂₀	—	2	1	no	—
312	D₂₀	—	2	1	no	—
313	D₂₀	#131	1	2	yes	—
314	D₂₀	#131	1	2	yes	—
315	C₄×D₅	—	4	1	no	—
316	C₄×D₅	—	4	1	no	—
317	C₄×D₅	—	4	1	no	—
318	C₄×D₅	—	4	1	no	—
319	C₄×D₅	—	8	1	no	—
320	C₄×D₅	—	8	1	no	—
321	C₅×C₈	—	4	1	no	—
322	C₅×C₈	—	4	1	no	—
323	C₅×C₈	—	4	1	no	—
324	C₅×C₈	—	4	1	no	—
325	#168	—	2	1	no	—
326	#168	—	2	1	no	—
327	#168	—	2	1	no	—
328	#168	—	2	1	no	—
329	#168	—	2	1	no	—
330	#168	—	2	1	no	—
331	#168	—	2	1	no	—
332	#168	—	2	1	no	—
333	#168	—	4	1	no	—
334	#168	—	4	1	no	—
335	C₂²×D₄	—	5	1	no	—
336	C₂³×C₄	—	10	1	no	—
337	C₂×SD₁₆	—	5	1	no	—
338	C₂×SD₁₆	—	5	1	no	—
339	C₂×D₈	—	5	1	no	—
340	C₂×D₈	—	5	1	no	—
341	C₂×M₁₆	—	10	1	no	—
342	C₂×M₁₆	—	10	1	no	—
343	C₂²×C₈	—	10	1	no	—
344	C₂²×C₈	—	10	1	no	—
345	C₂²×C₈	—	10	1	no	—
346	C₂²×C₈	—	10	1	no	—
347	C₂²×C₈	—	10	1	no	—
348	#126	—	2	1	no	—
349	#125	C₄×D₅	1	1	yes	characteristic
350	#124	C₄×D₅	1	1	yes	characteristic
351	#123	—	2	1	no	—
352	C₂²⋊Q₈	C₄×D₅	1	1	yes	characteristic
353	#121	C₄×D₅	1	1	yes	characteristic
354	C₄×Q₈	C₂²×D₅	1	1	yes	characteristic
355	C₄×D₄	—	2	1	no	—
356	C₄×D₄	—	5	1	no	—
357	C₄×D₄	—	5	1	no	—
358	C₄×D₄	—	5	1	no	—
359	C₄×D₄	—	5	1	no	—
360	C₄×D₄	—	10	1	no	—
361	C₄×D₄	—	10	1	no	—
362	C₄×D₄	C₂²×D₅	1	1	yes	characteristic
363	#117	—	2	1	no	—
364	C₂×C₄⋊C₄	—	5	1	no	—
365	C₂×C₂²⋊C₄	—	10	1	no	—
366	C₂×C₄²	C₂²×D₅	1	1	yes	characteristic
367	#107	—	5	1	no	—
368	#107	—	5	1	no	—
369	#106	—	5	1	no	—
370	#106	—	5	1	no	—
371	C₄⋊C₈	—	2	1	no	—
372	C₄⋊C₈	—	5	1	no	—
373	C₄⋊C₈	—	5	1	no	—
374	C₄⋊C₈	—	5	1	no	—
375	C₄⋊C₈	—	5	1	no	—
376	C₄⋊C₈	—	5	1	no	—
377	C₄⋊C₈	—	5	1	no	—
378	C₄⋊C₈	—	10	1	no	—
379	C₄⋊C₈	—	10	1	no	—
380	C₄⋊C₈	—	10	1	no	—
381	C₄⋊C₈	C₂²×D₅	1	1	yes	characteristic
382	C₄⋊C₈	C₂²×D₅	1	1	yes	characteristic
383	#103	—	5	1	no	—
384	#103	—	5	1	no	—
385	#102	—	5	1	no	—
386	#102	—	5	1	no	—
387	#102	—	5	1	no	—
388	#102	—	5	1	no	—
389	#102	—	5	1	no	—
390	#102	—	5	1	no	—
391	C₂²⋊C₈	—	2	1	no	—
392	C₂²⋊C₈	—	2	1	no	—
393	C₂²⋊C₈	—	5	1	no	—
394	C₂²⋊C₈	—	5	1	no	—
395	C₂²⋊C₈	—	5	1	no	—
396	C₂²⋊C₈	—	5	1	no	—
397	C₂²⋊C₈	—	10	1	no	—
398	C₂²⋊C₈	—	10	1	no	—
399	C₂²⋊C₈	—	10	1	no	—
400	C₂²⋊C₈	—	10	1	no	—
401	C₂²⋊C₈	—	10	1	no	—
402	C₂²⋊C₈	—	10	1	no	—
403	#97	—	10	1	no	—
404	C₄×C₈	—	2	1	no	—
405	C₄×C₈	—	5	1	no	—
406	C₄×C₈	—	5	1	no	—
407	C₄×C₈	—	5	1	no	—
408	C₄×C₈	—	5	1	no	—
409	C₄×C₈	—	10	1	no	—
410	C₄×C₈	C₂²×D₅	1	1	yes	characteristic
411	C₄×C₈	C₂²×D₅	1	1	yes	characteristic
412	C₂²×C₅	—	2	1	no	—
413	C₂²×C₅	—	2	1	no	—
414	C₂²×C₅	—	2	1	no	—
415	C₂²×C₅	—	4	1	no	—
416	C₂²×C₅	—	4	1	no	—
417	C₂²×C₅	—	4	1	no	—
418	C₂²×C₅	C₂×C₄×D₄	1	1	yes	characteristic
419	C₂×D₅	—	2	2	no	—
420	C₂×D₅	—	2	2	no	—
421	C₂×D₅	—	4	1	no	—
422	C₂×D₅	—	4	1	no	—
423	C₂×D₅	—	4	1	no	—
424	C₂×D₅	—	4	1	no	—
425	C₂×D₅	—	8	4	no	—
426	C₄×C₅	—	2	1	no	—
427	C₄×C₅	—	2	1	no	—
428	C₄×C₅	—	2	1	no	—
429	C₄×C₅	—	2	1	no	—
430	C₄×C₅	—	4	1	no	—
431	C₄×C₅	—	4	1	no	—
432	C₄×C₅	—	4	1	no	—
433	C₄×C₅	C₂×#131	1	1	yes	characteristic
434	C₄×C₅	C₂×#131	1	1	yes	characteristic
435	C₄×C₅	#576	1	1	yes	characteristic
436	C₄×C₅	#577	1	1	yes	characteristic
437	Dic₅	—	4	1	no	—
438	Dic₅	—	4	1	no	—
439	C₂⁴	—	10	1	no	—
440	C₂×Q₈	C₂×C₄×D₅	1	1	yes	characteristic
441	C₂×D₄	—	2	1	no	—
442	C₂×D₄	—	5	1	no	—
443	C₂×D₄	—	5	1	no	—
444	C₂×D₄	—	10	2	no	—
445	C₂×D₄	—	10	2	no	—
446	C₂×D₄	—	10	1	no	—
447	C₂×D₄	C₂×C₄×D₅	1	1	yes	characteristic
448	C₂²×C₄	—	2	1	no	—
449	C₂²×C₄	—	10	1	no	—
450	C₂²×C₄	—	10	1	no	—
451	C₂²×C₄	—	10	1	no	—
452	C₂²×C₄	—	10	1	no	—
453	C₂²×C₄	—	10	1	no	—
454	C₂²×C₄	—	40	1	no	—
455	C₂²×C₄	—	40	1	no	—
456	C₂²×C₄	C₂×C₄×D₅	1	1	yes	characteristic
457	C₂²×C₄	D₄×D₅	1	1	yes	characteristic
458	C₂²×C₄	#711	1	1	yes	characteristic
459	SD₁₆	—	10	2	no	—
460	SD₁₆	—	10	2	no	—
461	D₈	—	10	2	no	—
462	D₈	—	10	2	no	—
463	M₁₆	—	40	1	no	—
464	M₁₆	—	40	1	no	—
465	C₂×C₈	—	2	1	no	—
466	C₂×C₈	—	2	1	no	—
467	C₂×C₈	—	2	1	no	—
468	C₂×C₈	—	2	1	no	—
469	C₂×C₈	—	5	1	no	—
470	C₂×C₈	—	5	1	no	—
471	C₂×C₈	—	5	1	no	—
472	C₂×C₈	—	5	1	no	—
473	C₂×C₈	—	5	1	no	—
474	C₂×C₈	—	5	1	no	—
475	C₂×C₈	—	5	1	no	—
476	C₂×C₈	—	5	1	no	—
477	C₂×C₈	—	10	1	no	—
478	C₂×C₈	—	10	1	no	—
479	C₂×C₈	—	40	1	no	—
480	C₂×C₈	—	40	1	no	—
481	C₂×C₈	—	40	1	no	—
482	C₂×C₈	—	40	1	no	—
483	C₂×C₈	—	40	1	no	—
484	C₄⋊C₄	—	2	1	no	—
485	C₄⋊C₄	—	2	1	no	—
486	C₄⋊C₄	—	2	1	no	—
487	C₄⋊C₄	—	2	1	no	—
488	C₄⋊C₄	—	5	1	no	—
489	C₄⋊C₄	—	5	1	no	—
490	C₄⋊C₄	—	10	1	no	—
491	C₄⋊C₄	C₂×C₄×D₅	1	1	yes	characteristic
492	C₄⋊C₄	C₂×C₄×D₅	1	1	yes	characteristic
493	C₂²⋊C₄	—	2	1	no	—
494	C₂²⋊C₄	—	2	1	no	—
495	C₂²⋊C₄	—	2	1	no	—
496	C₂²⋊C₄	—	2	1	no	—
497	C₂²⋊C₄	—	2	1	no	—
498	C₂²⋊C₄	—	10	1	no	—
499	C₂²⋊C₄	—	10	1	no	—
500	C₂²⋊C₄	—	10	1	no	—
501	C₂²⋊C₄	—	10	1	no	—
502	C₄²	—	2	1	no	—
503	C₄²	C₂×C₄×D₅	1	1	yes	characteristic
504	C₄²	D₄×D₅	1	1	yes	characteristic
505	C₄²	#711	1	1	yes	characteristic
506	C₄²	C₂³×D₅	1	1	yes	characteristic
507	C₂×C₅	—	4	1	no	—
508	C₂×C₅	—	8	1	no	—
509	C₂×C₅	#2929	1	1	yes	characteristic
510	C₂×C₅	#2946	1	1	yes	characteristic
511	C₂×C₅	#2957	1	1	yes	characteristic
512	D₅	—	4	2	no	—
513	D₅	—	4	2	no	—
514	C₂³	—	2	1	no	—
515	C₂³	—	10	4	no	—
516	C₂³	—	10	1	no	—
517	C₂³	—	10	1	no	—
518	C₂³	—	40	1	no	—
519	C₂³	—	40	1	no	—
520	C₂³	#4027	1	1	yes	characteristic
521	Q₈	—	2	1	no	—
522	Q₈	—	2	1	no	—
523	D₄	—	2	1	no	—
524	D₄	—	2	1	no	—
525	D₄	—	5	2	no	—
526	D₄	—	5	2	no	—
527	D₄	—	8	1	no	—
528	D₄	—	10	4	no	—
529	D₄	—	10	1	no	—
530	D₄	—	10	1	no	—
531	C₂×C₄	—	2	1	no	—
532	C₂×C₄	—	2	1	no	—
533	C₂×C₄	—	2	1	no	—
534	C₂×C₄	—	2	1	no	—
535	C₂×C₄	—	2	1	no	—
536	C₂×C₄	—	2	1	no	—
537	C₂×C₄	—	2	1	no	—
538	C₂×C₄	—	4	1	no	—
539	C₂×C₄	—	4	1	no	—
540	C₂×C₄	—	4	1	no	—
541	C₂×C₄	—	10	1	no	—
542	C₂×C₄	—	10	1	no	—
543	C₂×C₄	—	20	1	no	—
544	C₂×C₄	—	20	1	no	—
545	C₂×C₄	—	20	1	no	—
546	C₂×C₄	—	20	1	no	—
547	C₂×C₄	—	40	1	no	—
548	C₂×C₄	—	40	1	no	—
549	C₂×C₄	—	40	1	no	—
550	C₂×C₄	#4027	1	1	yes	characteristic
551	C₂×C₄	#4027	1	1	yes	characteristic
552	C₂×C₄	#4027	1	1	yes	characteristic
553	C₂×C₄	C₂²×C₄×D₅	1	1	yes	characteristic
554	C₂×C₄	C₂×D₄×D₅	1	1	yes	characteristic
555	C₂×C₄	C₂×#711	1	1	yes	characteristic
556	C₈	—	4	1	no	—
557	C₈	—	4	1	no	—
558	C₈	—	4	1	no	—
559	C₈	—	4	1	no	—
560	C₈	—	10	1	no	—
561	C₈	—	10	1	no	—
562	C₈	—	10	1	no	—
563	C₈	—	10	1	no	—
564	C₈	—	10	1	no	—
565	C₈	—	10	1	no	—
566	C₈	—	10	1	no	—
567	C₈	—	10	1	no	—
568	C₈	—	20	1	no	—
569	C₈	—	20	1	no	—
570	C₅	#17918	1	1	yes	characteristic, complemented, Sylow
571	C₂²	—	2	1	no	—
572	C₂²	—	2	1	no	—
573	C₂²	—	2	1	no	—
574	C₂²	—	4	1	no	—
575	C₂²	—	4	1	no	—
576	C₂²	—	4	1	no	—
577	C₂²	—	10	2	no	—
578	C₂²	—	10	2	no	—
579	C₂²	—	20	1	no	—
580	C₂²	—	20	1	no	—
581	C₂²	—	20	1	no	—
582	C₂²	—	20	1	no	—
583	C₂²	—	40	4	no	—
584	C₂²	C₂×#4027	1	1	yes	characteristic
585	C₄	—	2	1	no	—
586	C₄	—	2	1	no	—
587	C₄	—	2	1	no	—
588	C₄	—	2	1	no	—
589	C₄	—	4	1	no	—
590	C₄	—	4	1	no	—
591	C₄	—	4	1	no	—
592	C₄	—	20	1	no	—
593	C₄	—	20	1	no	—
594	C₄	D₅×#131	1	1	yes	characteristic
595	C₄	D₅×#131	1	1	yes	characteristic
596	C₄	#66103	1	1	yes	characteristic
597	C₄	#66104	1	1	yes	characteristic
598	C₂	—	4	1	no	—
599	C₂	—	8	1	no	—
600	C₂	—	20	2	no	—
601	C₂	—	20	2	no	—
602	C₂	#10610386	1	1	yes	characteristic
603	C₂	#10610551	1	1	yes	characteristic
604	C₂	#10610721	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×#1482	C₂
socle	C₂²×C₅	C₂×C₄×D₄
prime radical	#65325	C₄
cosocle	C₄²×C₅	C₂⁴
hypercenter	#1482	D₅
hypocenter	C₅	#17918
LCS	G ▷ C₂×C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1482

Complements

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

N	H ≅ G/N	type
2. #10614862	C₂	semidirect
3. #10611017	C₂	semidirect
4. C₅×#1482	C₂	semidirect
5. #10601555	C₂	semidirect
6. #10601541	C₂	semidirect
7. #10601537	C₂	semidirect
8. #10599013	C₂	semidirect
9. #10599009	C₂	semidirect
10. #10599007	C₂	semidirect
11. #10599005	C₂	semidirect
12. #10598951	C₂	semidirect
13. #10598946	C₂	semidirect
14. #10598944	C₂	semidirect
15. #10598941	C₂	semidirect
30. #65313	C₂²	semidirect
31. Q₈×#168	C₂²	semidirect
35. #65301	C₂²	semidirect
37. D₄×#168	C₂²	semidirect
51. C₅×Q₈⋊C₈	C₂²	semidirect
52. C₅×Q₈⋊C₈	C₂²	semidirect
53. C₅×D₄⋊C₈	C₂²	semidirect
54. C₅×D₄⋊C₈	C₂²	semidirect
55. #64700	C₂²	semidirect
56. #64700	C₂²	semidirect
57. #64699	C₂²	semidirect
58. #64699	C₂²	semidirect
63. #64675	C₂²	semidirect
64. #64674	C₂²	semidirect
65. #64674	C₂²	semidirect
66. C₈×#168	C₂²	semidirect
158. #1482	D₅	semidirect
267. Q₈⋊C₈	C₂×D₅	semidirect
268. Q₈⋊C₈	C₂×D₅	semidirect
273. D₄⋊C₈	C₂×D₅	semidirect
274. D₄⋊C₈	C₂×D₅	semidirect
570. C₅	#17918	semidirect

Maximal subgroups

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

subgroup	index
#10614872	2
#10614862	2
#10611017	2
C₅×#1482	2
#10601555	2
#10601541	2
#10601537	2
#10599013	2
#10599009	2
#10599007	2
#10599005	2
#10598951	2
#10598946	2
#10598944	2
#10598941	2
#17918	5