Subgroups — #12069165

Order 1280.

774 conjugacy classes of subgroups.

The subgroup lattice has 642 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#10611321	C₂	1	1	yes	maximal, characteristic
2	#10611269	C₂	1	1	yes	maximal, characteristic, complemented
3	C₈×D₄×D₅	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#1581	C₂	1	1	yes	maximal, characteristic, complemented
5	D₈×#168	C₂	1	1	yes	maximal, characteristic, complemented
6	#10601655	C₂	1	1	yes	maximal, characteristic, complemented
7	#10601634	C₂	1	1	yes	maximal, characteristic, complemented
8	#10599365	C₂	1	1	yes	maximal, characteristic, complemented
9	#10599349	C₂	1	1	yes	maximal, characteristic, complemented
10	#10598965	C₂	1	1	yes	maximal, characteristic, complemented
11	#10598961	C₂	1	1	yes	maximal, characteristic, complemented
12	#10598941	C₂	1	1	yes	maximal, characteristic, complemented
13	#10598941	C₂	1	1	yes	maximal, characteristic, complemented
14	#10598871	C₂	1	1	yes	maximal, characteristic, complemented
15	#10598861	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#4053	—	2	1	no	—
17	C₂²×C₈×D₅	—	2	1	no	—
18	#65882	C₂²	1	1	yes	characteristic
19	C₄×D₄×D₅	C₂²	1	1	yes	characteristic
20	C₄×C₅×D₈	C₂²	1	1	yes	characteristic
21	C₅×#436	C₂²	1	1	yes	characteristic, complemented
22	C₅×C₈×D₄	C₂²	1	1	yes	characteristic
23	#65445	C₄	1	1	yes	characteristic
24	#65439	C₄	1	1	yes	characteristic
25	#65417	—	2	1	no	—
26	C₈×C₂²⋊D₅	—	2	1	no	—
27	C₄×#686	C₂²	1	1	yes	characteristic
28	C₄×#686	C₂²	1	1	yes	characteristic
29	D₄×#168	C₂²	1	1	yes	characteristic
30	D₄×#168	C₂²	1	1	yes	characteristic, complemented
31	#65179	C₄	1	1	yes	characteristic
32	#65171	C₄	1	1	yes	characteristic
33	#65126	C₂²	1	1	yes	characteristic
34	#65123	C₂²	1	1	yes	characteristic
35	#65123	C₂²	1	1	yes	characteristic, complemented
36	D₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
37	#65075	C₄	1	1	yes	characteristic
38	#65063	C₄	1	1	yes	characteristic
39	#65062	C₄	1	1	yes	characteristic
40	#65048	C₄	1	1	yes	characteristic
41	#65016	—	2	1	no	—
42	#65014	—	2	1	no	—
43	#65014	—	2	1	no	—
44	D₅×C₂²⋊C₈	—	2	1	no	—
45	C₄×D₄₀	C₂²	1	1	yes	characteristic
46	#64977	C₂²	1	1	yes	characteristic, complemented
47	C₈×D₂₀	C₂²	1	1	yes	characteristic
48	#64974	C₂²	1	1	yes	characteristic
49	#64974	C₂²	1	1	yes	characteristic
50	C₄×C₈×D₅	C₂²	1	1	yes	characteristic
51	C₅×#335	C₂²	1	1	yes	characteristic, complemented
52	C₅×D₄⋊C₈	C₂²	1	1	yes	characteristic
53	C₅×D₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
54	C₅×#322	C₂²	1	1	yes	characteristic, complemented
55	D₄⋊#168	C₂²	1	1	yes	characteristic
56	D₄⋊#168	C₂²	1	1	yes	characteristic, complemented
57	#64703	C₂²	1	1	yes	characteristic
58	#64703	C₂²	1	1	yes	characteristic, complemented
59	#64699	C₂²	1	1	yes	characteristic, complemented
60	#64699	C₂²	1	1	yes	characteristic, complemented
61	#64679	C₂²	1	1	yes	characteristic
62	#64679	C₂²	1	1	yes	characteristic, complemented
63	#64678	C₂²	1	1	yes	characteristic, complemented
64	#64675	C₂²	1	1	yes	characteristic, complemented
65	C₈×#168	C₂²	1	1	yes	characteristic, complemented
66	C₈×#168	C₂²	1	1	yes	characteristic, complemented
67	#17900	—	5	1	no	maximal, Sylow
68	C₂×D₄×D₅	C₂×C₄	1	1	yes	characteristic
69	C₂×#709	—	2	1	no	—
70	C₂²×C₄×D₅	—	2	1	no	—
71	C₂×C₅×D₈	C₂×C₄	1	1	yes	characteristic
72	C₂×C₅×M₁₆	—	2	1	no	—
73	C₂²×C₅×C₈	—	2	1	no	—
74	C₄×C₅×D₄	C₂³	1	1	yes	characteristic
75	C₄×C₅×D₄	C₂³	1	1	yes	characteristic
76	#4086	C₂×C₄	1	1	yes	characteristic
77	#4084	C₂×C₄	1	1	yes	characteristic
78	D₄×Dic₅	C₂×C₄	1	1	yes	characteristic
79	C₂×#686	C₂×C₄	1	1	yes	characteristic
80	C₂×#686	C₂×C₄	1	1	yes	characteristic
81	C₄×C₂²⋊D₅	—	2	1	no	—
82	C₄×C₂²⋊D₅	—	2	1	no	—
83	C₂²×#168	—	2	1	no	—
84	C₂²×#168	—	2	1	no	—
85	#4053	—	4	4	no	—
86	C₂×D₄₀	C₂×C₄	1	1	yes	characteristic
87	C₂×#676	—	2	1	no	—
88	C₂×#676	—	2	1	no	—
89	C₂×C₈×D₅	—	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	—	4	4	no	—
94	C₂×C₈×D₅	D₄	1	1	yes	characteristic
95	C₂×C₈×D₅	D₄	1	1	yes	characteristic
96	#4041	C₂×C₄	1	1	yes	characteristic
97	#4039	C₂×C₄	1	1	yes	characteristic
98	D₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
99	#4034	C₂×C₄	1	1	yes	characteristic
100	#4031	—	2	1	no	—
101	#4030	—	2	1	no	—
102	#4027	—	2	1	no	—
103	D₅×C₂²⋊C₄	—	2	1	no	—
104	C₄×D₂₀	C₂³	1	1	yes	characteristic
105	C₄×D₂₀	C₂³	1	1	yes	characteristic
106	C₄²×D₅	C₂³	1	1	yes	characteristic
107	C₅×#107	C₂×C₄	1	1	yes	characteristic
108	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
109	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
110	C₅×#102	C₂×C₄	1	1	yes	characteristic
111	C₅×#102	C₂×C₄	1	1	yes	characteristic
112	C₅×C₂²⋊C₈	—	2	1	no	—
113	C₅×C₂²⋊C₈	—	2	1	no	—
114	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
115	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
116	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
117	#3964	C₂×C₄	1	1	yes	characteristic
118	#3964	C₂×C₄	1	1	yes	characteristic
119	C₂²⋊#168	—	2	1	no	—
120	C₂²⋊#168	—	2	1	no	—
121	#3953	C₂×C₄	1	1	yes	characteristic
122	#3953	C₂×C₄	1	1	yes	characteristic
123	#3952	—	2	1	no	—
124	#3952	—	2	1	no	—
125	#3952	—	2	1	no	—
126	#3952	—	2	1	no	—
127	#3952	—	2	1	no	—
128	#3952	C₂×C₄	1	1	yes	characteristic
129	#3952	C₂×C₄	1	1	yes	characteristic
130	#3950	C₂×C₄	1	1	yes	characteristic
131	#3946	—	2	1	no	—
132	#3946	—	2	1	no	—
133	#3946	—	2	1	no	—
134	#3946	C₂×C₄	1	1	yes	characteristic
135	#3946	C₂×C₄	1	1	yes	characteristic
136	C₈×Dic₅	D₄	1	1	yes	characteristic
137	C₈×Dic₅	D₄	1	1	yes	characteristic
138	#3941	C₂×C₄	1	1	yes	characteristic
139	#3941	C₂×C₄	1	1	yes	characteristic
140	#3939	C₂×C₄	1	1	yes	characteristic
141	#3939	C₂×C₄	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	C₄×#168	C₂³	1	1	yes	characteristic
146	C₄×#168	C₂³	1	1	yes	characteristic
147	#3100	—	5	1	no	—
148	#2931	—	5	1	no	—
149	C₂×C₈×D₄	—	5	1	no	—
150	#1581	—	5	1	no	—
151	#1581	—	5	1	no	—
152	#1581	—	5	1	no	—
153	#1581	D₅	1	1	yes	characteristic, complemented
154	C₈×D₈	—	5	1	no	—
155	C₈×D₈	—	5	1	no	—
156	C₈×D₈	—	5	1	no	—
157	C₈×D₈	—	5	1	no	—
158	#1571	—	5	1	no	—
159	#1486	—	5	1	no	—
160	#1480	—	5	1	no	—
161	#1450	—	5	1	no	—
162	C₂³×D₅	—	2	1	no	—
163	C₂×C₅×D₄	C₂²×C₄	1	1	yes	characteristic
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	C₂×C₂²⋊D₅	—	2	1	no	—
168	C₂×C₂²⋊D₅	—	2	1	no	—
169	C₂×C₂²⋊D₅	—	2	1	no	—
170	C₂×C₂²⋊D₅	—	2	1	no	—
171	C₂²×Dic₅	—	2	1	no	—
172	D₄×D₅	—	2	2	no	—
173	D₄×D₅	—	2	2	no	—
174	#709	—	4	2	no	—
175	#709	—	4	2	no	—
176	C₂×D₂₀	—	2	1	no	—
177	C₂×D₂₀	C₂²×C₄	1	1	yes	characteristic
178	C₂×D₂₀	C₂²×C₄	1	1	yes	characteristic
179	C₂×C₄×D₅	—	2	1	no	—
180	C₂×C₄×D₅	—	2	1	no	—
181	C₂×C₄×D₅	—	2	1	no	—
182	C₂×C₄×D₅	—	2	1	no	—
183	C₂×C₄×D₅	—	4	2	no	—
184	C₂×C₄×D₅	—	4	2	no	—
185	C₂×C₄×D₅	C₂²×C₄	1	1	yes	characteristic
186	C₂×C₄×D₅	C₂×D₄	1	1	yes	characteristic
187	C₂×C₄×D₅	#41	1	1	yes	characteristic
188	C₂×Dic₁₀	—	2	1	no	—
189	C₅×D₈	—	2	2	no	—
190	C₅×M₁₆	—	4	2	no	—
191	C₂×C₅×C₈	—	2	1	no	—
192	C₂×C₅×C₈	—	2	1	no	—
193	C₂×C₅×C₈	—	2	1	no	—
194	C₂×C₅×C₈	—	4	2	no	—
195	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
196	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
197	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
198	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
199	C₅×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
200	C₅×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
201	C₅×C₂²⋊C₄	—	2	1	no	—
202	C₅×C₂²⋊C₄	—	2	1	no	—
203	C₄²×C₅	C₂⁴	1	1	yes	characteristic
204	C₂²⋊Dic₅	—	2	1	no	—
205	C₂²⋊Dic₅	—	2	1	no	—
206	#686	—	2	2	no	—
207	#686	—	2	2	no	—
208	#685	—	2	1	no	—
209	#685	—	2	1	no	—
210	#685	—	2	1	no	—
211	#685	—	2	1	no	—
212	C₄⋊Dic₅	C₂²×C₄	1	1	yes	characteristic
213	C₄⋊Dic₅	C₂²×C₄	1	1	yes	characteristic
214	#683	—	2	1	no	—
215	#683	—	2	1	no	—
216	C₄×Dic₅	C₂²×C₄	1	1	yes	characteristic
217	C₄×Dic₅	C₂×D₄	1	1	yes	characteristic
218	C₄×Dic₅	#41	1	1	yes	characteristic
219	C₂×#168	—	2	1	no	—
220	C₂×#168	—	2	1	no	—
221	C₂×#168	—	2	1	no	—
222	C₂×#168	—	4	2	no	—
223	C₂×#168	—	4	2	no	—
224	C₂×#168	C₂²×C₄	1	1	yes	characteristic
225	C₂×#168	C₂²×C₄	1	1	yes	characteristic
226	C₂×#168	C₂×D₄	1	1	yes	characteristic
227	C₂×#168	C₂×D₄	1	1	yes	characteristic
228	D₄₀	—	2	2	no	—
229	#676	—	4	2	no	—
230	#676	—	4	2	no	—
231	C₈×D₅	—	2	2	no	—
232	C₈×D₅	—	4	2	no	—
233	C₈×D₅	—	4	2	no	—
234	C₈×D₅	—	4	2	no	—
235	C₈×D₅	—	4	2	no	—
236	C₈×D₅	D₈	1	4	yes	complemented
237	C₂×#131	—	10	1	no	—
238	C₂³×C₈	—	10	1	no	—
239	#532	—	5	1	no	—
240	C₂×C₄×D₄	—	5	1	no	—
241	#480	—	5	1	no	—
242	#480	—	5	1	no	—
243	#474	—	5	1	no	—
244	#474	—	5	1	no	—
245	#459	—	5	1	no	—
246	#459	—	5	1	no	—
247	#447	—	5	1	no	—
248	#447	—	5	1	no	—
249	C₄×D₈	—	5	1	no	—
250	C₄×D₈	—	5	1	no	—
251	C₄×D₈	—	5	1	no	—
252	C₄×D₈	C₂×D₅	1	1	yes	characteristic
253	#436	—	5	1	no	—
254	#436	—	10	1	no	—
255	#436	C₂×D₅	1	1	yes	characteristic, complemented
256	C₈×D₄	—	5	1	no	—
257	C₈×D₄	—	5	1	no	—
258	C₈×D₄	—	5	1	no	—
259	C₈×D₄	—	5	1	no	—
260	C₈×D₄	—	5	1	no	—
261	C₈×D₄	—	10	1	no	—
262	C₈×D₄	—	10	1	no	—
263	C₈×D₄	—	10	1	no	—
264	C₈×D₄	C₂×D₅	1	1	yes	characteristic
265	#431	—	5	1	no	—
266	#431	—	5	1	no	—
267	#423	—	5	1	no	—
268	C₂×C₄⋊C₈	—	5	1	no	—
269	#408	—	10	1	no	—
270	C₂×C₂²⋊C₈	—	10	1	no	—
271	C₂×C₄×C₈	—	5	1	no	—
272	#335	—	5	1	no	—
273	#335	—	5	1	no	—
274	#335	—	5	1	no	—
275	#335	C₂×D₅	1	1	yes	characteristic, complemented
276	D₄⋊C₈	—	5	1	no	—
277	D₄⋊C₈	—	5	1	no	—
278	D₄⋊C₈	—	5	1	no	—
279	D₄⋊C₈	—	5	1	no	—
280	D₄⋊C₈	—	5	1	no	—
281	D₄⋊C₈	—	5	1	no	—
282	D₄⋊C₈	C₂×D₅	1	1	yes	characteristic
283	D₄⋊C₈	C₂×D₅	1	1	yes	characteristic, complemented
284	#322	—	5	1	no	—
285	#322	C₂×D₅	1	1	yes	characteristic, complemented
286	C₈²	—	5	1	no	—
287	C₈²	—	5	1	no	—
288	C₂³×C₅	—	2	1	no	—
289	C₂³×C₅	—	2	1	no	—
290	C₂²×D₅	—	2	4	no	—
291	C₂²×D₅	—	2	1	no	—
292	C₂²×D₅	—	2	1	no	—
293	C₂²×D₅	—	4	2	no	—
294	C₂²×D₅	—	4	2	no	—
295	C₂²×D₅	C₄×D₄	1	1	yes	characteristic
296	C₅×D₄	—	2	1	no	—
297	C₅×D₄	—	2	1	no	—
298	C₅×D₄	—	2	1	no	—
299	C₅×D₄	#131	1	2	yes	complemented
300	C₂×C₄×C₅	—	2	1	no	—
301	C₂×C₄×C₅	—	2	1	no	—
302	C₂×C₄×C₅	—	4	1	no	—
303	C₂×C₄×C₅	—	4	1	no	—
304	C₂×C₄×C₅	—	4	1	no	—
305	C₂×C₄×C₅	—	4	1	no	—
306	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
307	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
308	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
309	C₂²⋊D₅	—	2	4	no	—
310	C₂²⋊D₅	—	4	2	no	—
311	C₂²⋊D₅	—	4	2	no	—
312	C₂²⋊D₅	—	4	2	no	—
313	C₂×Dic₅	—	2	1	no	—
314	C₂×Dic₅	—	2	1	no	—
315	C₂×Dic₅	—	4	2	no	—
316	C₂×Dic₅	C₄×D₄	1	1	yes	characteristic
317	C₂×Dic₅	C₄×D₄	1	1	yes	characteristic
318	C₂×Dic₅	C₄×D₄	1	1	yes	characteristic
319	D₂₀	—	2	1	no	—
320	D₂₀	—	2	1	no	—
321	D₂₀	—	2	1	no	—
322	D₂₀	—	4	2	no	—
323	D₂₀	#131	1	2	yes	complemented
324	C₄×D₅	—	2	1	no	—
325	C₄×D₅	—	2	1	no	—
326	C₄×D₅	—	4	1	no	—
327	C₄×D₅	—	4	2	no	—
328	C₄×D₅	—	4	1	no	—
329	C₄×D₅	—	4	1	no	—
330	C₄×D₅	—	4	1	no	—
331	C₄×D₅	—	4	1	no	—
332	C₄×D₅	—	4	2	no	—
333	C₄×D₅	C₂×D₈	1	2	yes	—
334	C₄×D₅	#135	1	2	yes	—
335	Dic₁₀	—	4	2	no	—
336	C₅×C₈	—	2	1	no	—
337	C₅×C₈	—	2	1	no	—
338	C₅×C₈	—	2	1	no	—
339	C₅×C₈	—	4	1	no	—
340	C₅×C₈	—	4	1	no	—
341	C₅×C₈	—	4	1	no	—
342	C₅×C₈	C₂×D₈	1	2	yes	—
343	#168	—	2	1	no	—
344	#168	—	2	1	no	—
345	#168	—	2	1	no	—
346	#168	—	4	1	no	—
347	#168	—	4	1	no	—
348	#168	—	4	1	no	—
349	#168	C₂×D₈	1	2	yes	—
350	C₂×#41	—	10	1	no	—
351	C₂²×D₄	—	5	1	no	—
352	C₂³×C₄	—	10	1	no	—
353	C₂×D₈	—	5	1	no	—
354	C₂×D₈	—	5	1	no	—
355	C₂×D₈	—	5	1	no	—
356	C₂×D₈	C₄×D₅	1	1	yes	characteristic
357	#131	—	20	4	no	—
358	C₂×M₁₆	—	2	1	no	—
359	C₂×M₁₆	—	10	1	no	—
360	C₂×M₁₆	—	10	1	no	—
361	C₂²×C₈	—	2	1	no	—
362	C₂²×C₈	—	5	1	no	—
363	C₂²×C₈	—	5	1	no	—
364	C₂²×C₈	—	10	1	no	—
365	C₂²×C₈	—	10	1	no	—
366	C₂²×C₈	—	10	1	no	—
367	C₂²×C₈	—	10	1	no	—
368	C₂²×C₈	—	10	1	no	—
369	C₂²×C₈	—	10	1	no	—
370	C₂²×C₈	—	20	4	no	—
371	C₄⋊Q₈	—	5	1	no	—
372	#127	—	5	1	no	—
373	#124	—	10	1	no	—
374	#121	—	5	1	no	—
375	#121	—	5	1	no	—
376	#121	—	10	1	no	—
377	C₄×D₄	—	5	1	no	—
378	C₄×D₄	—	5	1	no	—
379	C₄×D₄	—	5	1	no	—
380	C₄×D₄	—	5	1	no	—
381	C₄×D₄	—	10	1	no	—
382	C₄×D₄	—	10	1	no	—
383	C₄×D₄	—	10	1	no	—
384	C₄×D₄	C₂²×D₅	1	1	yes	characteristic
385	C₄×D₄	C₂²×D₅	1	1	yes	characteristic
386	C₂×C₄⋊C₄	—	5	1	no	—
387	C₂×C₂²⋊C₄	—	10	1	no	—
388	C₂×C₄²	—	5	1	no	—
389	#107	—	5	1	no	—
390	#107	—	5	1	no	—
391	#107	—	5	1	no	—
392	#107	C₄×D₅	1	1	yes	characteristic
393	C₄⋊C₈	—	5	1	no	—
394	C₄⋊C₈	—	5	1	no	—
395	C₄⋊C₈	—	5	1	no	—
396	C₄⋊C₈	—	5	1	no	—
397	C₄⋊C₈	—	10	1	no	—
398	C₄⋊C₈	—	10	1	no	—
399	C₄⋊C₈	—	10	1	no	—
400	C₄⋊C₈	C₂²×D₅	1	1	yes	characteristic
401	C₄⋊C₈	C₂²×D₅	1	1	yes	characteristic
402	#102	—	5	1	no	—
403	#102	—	5	1	no	—
404	#102	—	5	1	no	—
405	#102	—	5	1	no	—
406	#102	—	5	1	no	—
407	#102	—	5	1	no	—
408	#102	C₄×D₅	1	1	yes	characteristic
409	#102	C₄×D₅	1	1	yes	characteristic
410	C₂²⋊C₈	—	2	1	no	—
411	C₂²⋊C₈	—	2	1	no	—
412	C₂²⋊C₈	—	5	1	no	—
413	C₂²⋊C₈	—	5	1	no	—
414	C₂²⋊C₈	—	10	1	no	—
415	C₂²⋊C₈	—	10	1	no	—
416	C₂²⋊C₈	—	10	1	no	—
417	C₂²⋊C₈	—	10	1	no	—
418	C₂²⋊C₈	—	10	1	no	—
419	C₂²⋊C₈	—	10	1	no	—
420	C₂²⋊C₈	—	10	1	no	—
421	C₄×C₈	—	5	1	no	—
422	C₄×C₈	—	5	1	no	—
423	C₄×C₈	—	5	1	no	—
424	C₄×C₈	—	5	1	no	—
425	C₄×C₈	—	5	1	no	—
426	C₄×C₈	C₂²×D₅	1	1	yes	characteristic
427	C₄×C₈	C₂²×D₅	1	1	yes	characteristic
428	C₄×C₈	C₂²×D₅	1	1	yes	characteristic
429	C₂²×C₅	—	2	2	no	—
430	C₂²×C₅	—	4	1	no	—
431	C₂²×C₅	—	4	1	no	—
432	C₂²×C₅	—	4	1	no	—
433	C₂²×C₅	—	4	1	no	—
434	C₂²×C₅	—	4	1	no	—
435	C₂²×C₅	C₂×C₄×D₄	1	1	yes	characteristic
436	C₂×D₅	—	2	1	no	—
437	C₂×D₅	—	2	1	no	—
438	C₂×D₅	—	2	2	no	—
439	C₂×D₅	—	4	8	no	—
440	C₂×D₅	—	4	1	no	—
441	C₂×D₅	—	4	1	no	—
442	C₂×D₅	—	4	1	no	—
443	C₂×D₅	—	4	1	no	—
444	C₂×D₅	—	4	1	no	—
445	C₂×D₅	C₄×D₈	1	2	yes	—
446	C₄×C₅	—	2	1	no	—
447	C₄×C₅	—	4	1	no	—
448	C₄×C₅	—	4	1	no	—
449	C₄×C₅	C₂×#131	1	1	yes	characteristic
450	C₄×C₅	C₂×#131	1	1	yes	characteristic
451	C₄×C₅	C₂²×D₈	1	1	yes	characteristic
452	C₄×C₅	C₂×#135	1	1	yes	characteristic
453	Dic₅	—	2	1	no	—
454	Dic₅	—	2	1	no	—
455	Dic₅	—	4	1	no	—
456	Dic₅	—	4	1	no	—
457	Dic₅	C₄×D₈	1	2	yes	—
458	C₂⁴	—	10	1	no	—
459	#41	—	20	2	no	—
460	#41	—	20	2	no	—
461	C₂×Q₈	—	10	1	no	—
462	C₂×D₄	—	5	1	no	—
463	C₂×D₄	—	5	1	no	—
464	C₂×D₄	—	10	1	no	—
465	C₂×D₄	—	10	1	no	—
466	C₂×D₄	—	10	1	no	—
467	C₂×D₄	—	10	1	no	—
468	C₂×D₄	—	10	2	no	—
469	C₂×D₄	—	10	2	no	—
470	C₂×D₄	—	10	1	no	—
471	C₂×D₄	C₂×C₄×D₅	1	1	yes	characteristic
472	C₂×D₄	C₂×C₄×D₅	1	1	yes	characteristic
473	C₂²×C₄	—	2	1	no	—
474	C₂²×C₄	—	2	1	no	—
475	C₂²×C₄	—	5	1	no	—
476	C₂²×C₄	—	5	1	no	—
477	C₂²×C₄	—	5	1	no	—
478	C₂²×C₄	—	10	1	no	—
479	C₂²×C₄	—	10	1	no	—
480	C₂²×C₄	—	10	1	no	—
481	C₂²×C₄	—	10	1	no	—
482	C₂²×C₄	—	10	1	no	—
483	C₂²×C₄	—	20	2	no	—
484	C₂²×C₄	—	20	2	no	—
485	D₈	—	2	2	no	—
486	D₈	—	10	2	no	—
487	D₈	—	10	2	no	—
488	D₈	—	10	2	no	—
489	M₁₆	—	4	2	no	—
490	M₁₆	—	20	2	no	—
491	M₁₆	—	20	2	no	—
492	C₂×C₈	—	2	1	no	—
493	C₂×C₈	—	2	1	no	—
494	C₂×C₈	—	2	1	no	—
495	C₂×C₈	—	4	2	no	—
496	C₂×C₈	—	5	1	no	—
497	C₂×C₈	—	5	4	no	—
498	C₂×C₈	—	5	1	no	—
499	C₂×C₈	—	5	1	no	—
500	C₂×C₈	—	5	1	no	—
501	C₂×C₈	—	10	2	no	—
502	C₂×C₈	—	10	1	no	—
503	C₂×C₈	—	10	1	no	—
504	C₂×C₈	—	10	1	no	—
505	C₂×C₈	—	20	2	no	—
506	C₂×C₈	—	20	2	no	—
507	C₂×C₈	—	20	2	no	—
508	C₂×C₈	—	20	2	no	—
509	C₂×C₈	—	20	2	no	—
510	C₂×C₈	—	20	2	no	—
511	C₂×C₈	C₂×C₄×D₅	1	1	yes	characteristic
512	C₂×C₈	C₂×C₄×D₅	1	1	yes	characteristic
513	C₂×C₈	D₄×D₅	1	1	yes	characteristic
514	C₂×C₈	D₄×D₅	1	1	yes	characteristic
515	C₄⋊C₄	—	5	1	no	—
516	C₄⋊C₄	—	5	1	no	—
517	C₄⋊C₄	—	10	1	no	—
518	C₄⋊C₄	—	10	1	no	—
519	C₄⋊C₄	C₂×C₄×D₅	1	1	yes	characteristic
520	C₄⋊C₄	C₂×C₄×D₅	1	1	yes	characteristic
521	C₂²⋊C₄	—	2	1	no	—
522	C₂²⋊C₄	—	2	1	no	—
523	C₂²⋊C₄	—	10	1	no	—
524	C₂²⋊C₄	—	10	1	no	—
525	C₂²⋊C₄	—	10	1	no	—
526	C₂²⋊C₄	—	10	1	no	—
527	C₂²⋊C₄	—	10	1	no	—
528	C₂²⋊C₄	—	10	1	no	—
529	C₄²	—	5	1	no	—
530	C₄²	—	5	1	no	—
531	C₄²	—	5	1	no	—
532	C₄²	C₂³×D₅	1	1	yes	characteristic
533	C₂×C₅	—	4	2	no	—
534	C₂×C₅	—	8	1	no	—
535	C₂×C₅	#2929	1	1	yes	characteristic
536	C₂×C₅	C₂×C₄×D₈	1	1	yes	characteristic
537	C₂×C₅	#2955	1	1	yes	characteristic
538	D₅	—	2	2	no	—
539	D₅	—	4	2	no	—
540	D₅	—	8	1	no	—
541	C₂³	—	2	1	no	—
542	C₂³	—	2	1	no	—
543	C₂³	—	5	1	no	—
544	C₂³	—	10	4	no	—
545	C₂³	—	10	1	no	—
546	C₂³	—	10	1	no	—
547	C₂³	—	20	2	no	—
548	C₂³	—	20	2	no	—
549	Q₈	—	20	2	no	—
550	D₄	—	2	1	no	—
551	D₄	—	2	1	no	—
552	D₄	—	2	1	no	—
553	D₄	—	5	2	no	—
554	D₄	—	10	4	no	—
555	D₄	—	10	1	no	—
556	D₄	—	10	1	no	—
557	D₄	—	10	1	no	—
558	D₄	—	20	2	no	—
559	D₄	—	20	2	no	—
560	D₄	—	20	2	no	—
561	D₄	—	20	2	no	—
562	D₄	#4053	1	2	yes	complemented
563	C₂×C₄	—	2	1	no	—
564	C₂×C₄	—	2	1	no	—
565	C₂×C₄	—	4	1	no	—
566	C₂×C₄	—	4	1	no	—
567	C₂×C₄	—	4	1	no	—
568	C₂×C₄	—	4	1	no	—
569	C₂×C₄	—	5	1	no	—
570	C₂×C₄	—	5	2	no	—
571	C₂×C₄	—	5	2	no	—
572	C₂×C₄	—	5	1	no	—
573	C₂×C₄	—	5	1	no	—
574	C₂×C₄	—	10	1	no	—
575	C₂×C₄	—	10	1	no	—
576	C₂×C₄	—	10	1	no	—
577	C₂×C₄	—	10	1	no	—
578	C₂×C₄	—	20	1	no	—
579	C₂×C₄	—	20	2	no	—
580	C₂×C₄	—	20	2	no	—
581	C₂×C₄	—	20	2	no	—
582	C₂×C₄	—	20	1	no	—
583	C₂×C₄	—	20	1	no	—
584	C₂×C₄	—	20	1	no	—
585	C₂×C₄	—	20	1	no	—
586	C₂×C₄	C₂²×C₄×D₅	1	1	yes	characteristic
587	C₂×C₄	C₂×D₄×D₅	1	1	yes	characteristic
588	C₂×C₄	D₅×#41	1	1	yes	characteristic
589	C₈	—	2	1	no	—
590	C₈	—	2	1	no	—
591	C₈	—	2	1	no	—
592	C₈	—	4	1	no	—
593	C₈	—	4	1	no	—
594	C₈	—	4	1	no	—
595	C₈	—	5	2	no	—
596	C₈	—	10	1	no	—
597	C₈	—	10	1	no	—
598	C₈	—	10	1	no	—
599	C₈	—	20	1	no	—
600	C₈	—	20	1	no	—
601	C₈	—	20	1	no	—
602	C₈	D₅×D₈	1	2	yes	—
603	C₅	#17900	1	1	yes	characteristic, complemented, Sylow
604	C₂²	—	2	2	no	—
605	C₂²	—	4	1	no	—
606	C₂²	—	4	1	no	—
607	C₂²	—	4	1	no	—
608	C₂²	—	4	1	no	—
609	C₂²	—	4	1	no	—
610	C₂²	—	5	2	no	—
611	C₂²	—	10	1	no	—
612	C₂²	—	10	1	no	—
613	C₂²	—	10	2	no	—
614	C₂²	—	20	8	no	—
615	C₂²	—	20	1	no	—
616	C₂²	—	20	1	no	—
617	C₂²	—	20	1	no	—
618	C₂²	—	20	1	no	—
619	C₂²	—	20	1	no	—
620	C₂²	C₄×D₄×D₅	1	1	yes	characteristic
621	C₄	—	2	1	no	—
622	C₄	—	4	1	no	—
623	C₄	—	4	1	no	—
624	C₄	—	5	2	no	—
625	C₄	—	10	1	no	—
626	C₄	—	10	1	no	—
627	C₄	—	20	1	no	—
628	C₄	—	20	1	no	—
629	C₄	C₂×#4053	1	1	yes	characteristic
630	C₄	D₅×#131	1	1	yes	characteristic
631	C₄	C₂×D₅×D₈	1	1	yes	characteristic
632	C₄	D₅×#135	1	1	yes	characteristic
633	C₂	—	4	2	no	—
634	C₂	—	8	1	no	—
635	C₂	—	10	2	no	—
636	C₂	—	20	2	no	—
637	C₂	—	40	1	no	—
638	C₂	#10611209	1	1	yes	characteristic
639	C₂	C₄×D₅×D₈	1	1	yes	characteristic
640	C₂	#10611628	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×#1581	C₂
socle	C₂²×C₅	C₂×C₄×D₄
prime radical	#10611321	C₂
cosocle	C₄²×C₅	C₂⁴
hypercenter	#1581	D₅
hypocenter	C₅	#17900
LCS	G ▷ C₂×C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₄ ◁ C₄×C₈ ◁ #1581

Complements

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

N	H ≅ G/N	type
2. #10611269	C₂	semidirect
3. C₈×D₄×D₅	C₂	semidirect
4. C₅×#1581	C₂	semidirect
5. D₈×#168	C₂	semidirect
6. #10601655	C₂	semidirect
7. #10601634	C₂	semidirect
8. #10599365	C₂	semidirect
9. #10599349	C₂	semidirect
10. #10598965	C₂	semidirect
11. #10598961	C₂	semidirect
12. #10598941	C₂	semidirect
13. #10598941	C₂	semidirect
14. #10598871	C₂	semidirect
15. #10598861	C₂	semidirect
21. C₅×#436	C₂²	semidirect
30. D₄×#168	C₂²	semidirect
35. #65123	C₂²	semidirect
46. #64977	C₂²	semidirect
51. C₅×#335	C₂²	semidirect
53. C₅×D₄⋊C₈	C₂²	semidirect
54. C₅×#322	C₂²	semidirect
56. D₄⋊#168	C₂²	semidirect
58. #64703	C₂²	semidirect
59. #64699	C₂²	semidirect
60. #64699	C₂²	semidirect
62. #64679	C₂²	semidirect
63. #64678	C₂²	semidirect
64. #64675	C₂²	semidirect
65. C₈×#168	C₂²	semidirect
66. C₈×#168	C₂²	semidirect
153. #1581	D₅	semidirect
236. C₈×D₅	D₈	semidirect
255. #436	C₂×D₅	semidirect
275. #335	C₂×D₅	semidirect
283. D₄⋊C₈	C₂×D₅	semidirect
285. #322	C₂×D₅	semidirect
299. C₅×D₄	#131	semidirect
323. D₂₀	#131	semidirect
562. D₄	#4053	semidirect
603. C₅	#17900	semidirect

Maximal subgroups

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

subgroup	index
#10611321	2
#10611269	2
C₈×D₄×D₅	2
C₅×#1581	2
D₈×#168	2
#10601655	2
#10601634	2
#10599365	2
#10599349	2
#10598965	2
#10598961	2
#10598941	2
#10598871	2
#10598861	2
#17900	5