Subgroups — #12070719

Order 1280.

794 conjugacy classes of subgroups.

The subgroup lattice has 658 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×D₅×D₈	C₂	1	1	yes	maximal, characteristic
2	#10611271	C₂	1	1	yes	maximal, characteristic, complemented
3	D₄×#676	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#1581	C₂	1	1	yes	maximal, characteristic, complemented
5	#10601672	C₂	1	1	yes	maximal, characteristic, complemented
6	#10601652	C₂	1	1	yes	maximal, characteristic, complemented
7	C₈×#686	C₂	1	1	yes	maximal, characteristic, complemented
8	#10599362	C₂	1	1	yes	maximal, characteristic, complemented
9	#10599352	C₂	1	1	yes	maximal, characteristic, complemented
10	#10598965	C₂	1	1	yes	maximal, characteristic, complemented
11	#10598965	C₂	1	1	yes	maximal, characteristic, complemented
12	#10598953	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	#10598860	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×D₅×D₈	C₄	1	1	yes	characteristic
17	C₂×D₅×M₁₆	—	2	1	no	—
18	C₂²×#676	—	2	1	no	—
19	C₄×D₄×D₅	C₂²	1	1	yes	characteristic
20	C₄×D₄×D₅	C₂²	1	1	yes	characteristic
21	C₄×C₅×D₈	C₂²	1	1	yes	characteristic
22	C₅×#436	C₂²	1	1	yes	characteristic, complemented
23	C₅×C₈×D₄	C₂²	1	1	yes	characteristic, complemented
24	D₈×Dic₅	C₄	1	1	yes	characteristic
25	#65416	—	2	1	no	—
26	#65400	—	2	1	no	—
27	C₄×#686	C₂²	1	1	yes	characteristic
28	C₄×#686	C₂²	1	1	yes	characteristic
29	#65301	C₂²	1	1	yes	characteristic, complemented
30	D₄×#168	C₂²	1	1	yes	characteristic, complemented
31	D₅×#107	C₄	1	1	yes	characteristic
32	#65161	C₄	1	1	yes	characteristic
33	#65127	C₂²	1	1	yes	characteristic, complemented
34	#65126	C₂²	1	1	yes	characteristic
35	#65126	C₂²	1	1	yes	characteristic
36	#65123	C₂²	1	1	yes	characteristic, complemented
37	D₅×#102	C₄	1	1	yes	characteristic
38	D₅×#102	C₄	1	1	yes	characteristic
39	#65045	C₄	1	1	yes	characteristic
40	#65045	C₄	1	1	yes	characteristic
41	#65019	—	2	1	no	—
42	#65017	—	2	1	no	—
43	#65015	—	2	1	no	—
44	#65015	—	2	1	no	—
45	C₄×D₄₀	C₂²	1	1	yes	characteristic
46	#64977	C₂²	1	1	yes	characteristic, complemented
47	C₄×#676	C₂²	1	1	yes	characteristic
48	C₈×D₂₀	C₂²	1	1	yes	characteristic, complemented
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, complemented
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, complemented
56	D₄⋊#168	C₂²	1	1	yes	characteristic, complemented
57	#64703	C₂²	1	1	yes	characteristic, complemented
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, complemented
62	#64679	C₂²	1	1	yes	characteristic, complemented
63	#64678	C₂²	1	1	yes	characteristic, complemented
64	#64674	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	M₁₆×D₈	—	5	1	no	maximal, Sylow
68	C₂×D₄×D₅	C₂×C₄	1	1	yes	characteristic
69	C₂×D₄×D₅	C₂×C₄	1	1	yes	characteristic
70	C₂²×C₄×D₅	—	2	1	no	—
71	C₂²×C₄×D₅	—	2	1	no	—
72	C₂×C₅×D₈	C₂×C₄	1	1	yes	characteristic
73	C₂×C₅×M₁₆	—	2	1	no	—
74	C₂²×C₅×C₈	—	2	1	no	—
75	C₄×C₅×D₄	C₂³	1	1	yes	characteristic
76	C₄×C₅×D₄	C₂³	1	1	yes	characteristic
77	D₄×Dic₅	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	C₂×#681	—	2	1	no	—
84	C₂²×#168	—	2	1	no	—
85	D₅×D₈	—	2	4	no	—
86	D₅×M₁₆	—	4	4	no	—
87	C₂×D₄₀	C₂×C₄	1	1	yes	characteristic
88	C₂×#676	—	2	1	no	—
89	C₂×#676	—	2	1	no	—
90	C₂×#676	—	2	1	no	—
91	C₂×#676	—	2	1	no	—
92	C₂×#676	—	4	4	no	—
93	C₂×#676	D₄	1	1	yes	characteristic
94	C₂×#676	D₄	1	1	yes	characteristic
95	C₂×C₈×D₅	—	2	1	no	—
96	C₂×C₈×D₅	—	2	1	no	—
97	C₂×C₈×D₅	C₂×C₄	1	1	yes	characteristic
98	C₂×C₈×D₅	C₂×C₄	1	1	yes	characteristic
99	#4039	C₂×C₄	1	1	yes	characteristic
100	#4039	C₂×C₄	1	1	yes	characteristic
101	D₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
102	D₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
103	#4027	—	2	1	no	—
104	#4027	—	2	1	no	—
105	D₅×C₂²⋊C₄	—	2	1	no	—
106	D₅×C₂²⋊C₄	—	2	1	no	—
107	C₄×D₂₀	C₂³	1	1	yes	characteristic
108	C₄×D₂₀	C₂³	1	1	yes	characteristic
109	C₄²×D₅	C₂³	1	1	yes	characteristic
110	C₅×#107	C₂×C₄	1	1	yes	characteristic
111	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
112	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
113	C₅×#102	C₂×C₄	1	1	yes	characteristic
114	C₅×#102	C₂×C₄	1	1	yes	characteristic
115	C₅×C₂²⋊C₈	—	2	1	no	—
116	C₅×C₂²⋊C₈	—	2	1	no	—
117	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
118	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
119	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
120	#3964	C₂×C₄	1	1	yes	characteristic
121	#3964	C₂×C₄	1	1	yes	characteristic
122	C₂²⋊#168	—	2	1	no	—
123	C₂²⋊#168	—	2	1	no	—
124	#3953	C₂×C₄	1	1	yes	characteristic
125	#3953	C₂×C₄	1	1	yes	characteristic
126	#3952	—	2	1	no	—
127	#3952	—	2	1	no	—
128	#3952	—	2	1	no	—
129	#3952	—	2	1	no	—
130	#3952	—	2	1	no	—
131	#3950	C₂×C₄	1	1	yes	characteristic
132	#3947	D₄	1	1	yes	characteristic
133	#3947	D₄	1	1	yes	characteristic
134	#3946	—	2	1	no	—
135	#3946	—	2	1	no	—
136	#3946	—	2	1	no	—
137	C₈×Dic₅	C₂×C₄	1	1	yes	characteristic
138	C₈×Dic₅	C₂×C₄	1	1	yes	characteristic
139	#3941	C₂×C₄	1	1	yes	characteristic
140	#3941	C₂×C₄	1	1	yes	characteristic
141	#3939	C₂×C₄	1	1	yes	characteristic
142	#3939	C₂×C₄	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	C₄×#168	C₂³	1	1	yes	characteristic
148	C₂×C₄×D₈	—	5	1	no	—
149	D₄×M₁₆	—	5	1	no	—
150	D₄×M₁₆	—	5	1	no	—
151	#1589	—	5	1	no	—
152	#1589	—	5	1	no	—
153	#1581	—	5	1	no	—
154	#1581	—	5	1	no	—
155	#1581	—	5	1	no	—
156	#1581	D₅	1	1	yes	characteristic, complemented
157	C₈×D₈	—	5	1	no	—
158	C₈×D₈	—	5	1	no	—
159	#1567	—	5	1	no	—
160	#1486	—	5	1	no	—
161	#1486	—	5	1	no	—
162	C₈×M₁₆	—	5	1	no	—
163	C₂³×D₅	—	2	1	no	—
164	C₂³×D₅	—	2	1	no	—
165	C₂×C₅×D₄	C₂²×C₄	1	1	yes	characteristic
166	C₂×C₅×D₄	C₂²×C₄	1	1	yes	characteristic
167	C₂²×C₄×C₅	—	2	1	no	—
168	C₂²×C₄×C₅	—	2	1	no	—
169	C₂×C₂²⋊D₅	—	2	1	no	—
170	C₂×C₂²⋊D₅	—	2	1	no	—
171	C₂²×Dic₅	—	2	1	no	—
172	C₂²×Dic₅	—	2	1	no	—
173	D₄×D₅	—	2	2	no	—
174	D₄×D₅	—	2	2	no	—
175	D₄×D₅	—	4	1	no	—
176	D₄×D₅	—	4	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	—	2	1	no	—
184	C₂×C₄×D₅	—	2	1	no	—
185	C₂×C₄×D₅	—	4	2	no	—
186	C₂×C₄×D₅	—	4	2	no	—
187	C₂×C₄×D₅	—	4	2	no	—
188	C₂×C₄×D₅	—	4	2	no	—
189	C₂×C₄×D₅	C₂²×C₄	1	1	yes	characteristic
190	C₂×C₄×D₅	C₂×D₄	1	1	yes	characteristic
191	C₂×C₄×D₅	#41	1	1	yes	characteristic
192	C₅×D₈	—	2	2	no	—
193	C₅×M₁₆	—	4	2	no	—
194	C₂×C₅×C₈	—	2	1	no	—
195	C₂×C₅×C₈	—	2	1	no	—
196	C₂×C₅×C₈	—	2	1	no	—
197	C₂×C₅×C₈	—	4	2	no	—
198	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
199	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
200	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
201	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
202	C₅×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
203	C₅×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
204	C₅×C₂²⋊C₄	—	2	1	no	—
205	C₅×C₂²⋊C₄	—	2	1	no	—
206	C₄²×C₅	C₂⁴	1	1	yes	characteristic
207	C₂²⋊Dic₅	—	2	1	no	—
208	C₂²⋊Dic₅	—	2	1	no	—
209	#686	—	2	2	no	—
210	#686	M₁₆	1	4	yes	complemented
211	#685	—	2	1	no	—
212	#685	—	2	1	no	—
213	#685	—	2	1	no	—
214	#685	—	2	1	no	—
215	C₄⋊Dic₅	C₂²×C₄	1	1	yes	characteristic
216	C₄⋊Dic₅	C₂²×C₄	1	1	yes	characteristic
217	#683	—	2	1	no	—
218	#683	—	2	1	no	—
219	C₄×Dic₅	C₂²×C₄	1	1	yes	characteristic
220	C₄×Dic₅	C₂×D₄	1	1	yes	characteristic
221	C₄×Dic₅	#41	1	1	yes	characteristic
222	#681	—	4	2	no	—
223	C₂×#168	—	2	1	no	—
224	C₂×#168	—	2	1	no	—
225	C₂×#168	—	2	1	no	—
226	C₂×#168	—	4	2	no	—
227	C₂×#168	C₂²×C₄	1	1	yes	characteristic
228	C₂×#168	C₂²×C₄	1	1	yes	characteristic
229	C₂×#168	C₂×D₄	1	1	yes	characteristic
230	C₂×#168	C₂×D₄	1	1	yes	characteristic
231	D₄₀	—	2	2	no	—
232	#676	—	2	2	no	—
233	#676	—	4	2	no	—
234	#676	—	4	2	no	—
235	#676	—	4	2	no	—
236	#676	—	4	2	no	—
237	#676	D₈	1	4	yes	complemented
238	C₈×D₅	—	2	2	no	—
239	C₈×D₅	—	4	1	no	—
240	C₈×D₅	—	4	2	no	—
241	C₈×D₅	—	4	2	no	—
242	C₂²×D₈	—	5	1	no	—
243	C₂²×M₁₆	—	10	1	no	—
244	C₂²×M₁₆	—	10	1	no	—
245	C₂×C₄×D₄	—	5	1	no	—
246	C₂×C₄×D₄	—	5	1	no	—
247	C₄×D₈	—	5	1	no	—
248	C₄×D₈	—	5	1	no	—
249	C₄×D₈	—	5	1	no	—
250	C₄×D₈	—	5	1	no	—
251	C₄×D₈	—	5	1	no	—
252	C₄×D₈	—	5	1	no	—
253	C₄×D₈	—	5	1	no	—
254	C₄×D₈	C₂×D₅	1	1	yes	characteristic
255	#436	—	5	1	no	—
256	#436	—	5	1	no	—
257	#436	—	5	1	no	—
258	#436	C₂×D₅	1	1	yes	characteristic, complemented
259	#435	—	10	1	no	—
260	#435	—	10	1	no	—
261	#435	—	10	1	no	—
262	#435	—	10	1	no	—
263	C₈×D₄	—	5	1	no	—
264	C₈×D₄	—	5	1	no	—
265	C₈×D₄	—	5	1	no	—
266	C₈×D₄	C₂×D₅	1	1	yes	characteristic, complemented
267	#431	—	5	1	no	—
268	C₂×#107	—	5	1	no	—
269	#423	—	5	1	no	—
270	#423	—	5	1	no	—
271	C₂×#102	—	5	1	no	—
272	C₂×#102	—	5	1	no	—
273	#407	—	10	1	no	—
274	#407	—	10	1	no	—
275	C₄×M₁₆	—	5	1	no	—
276	C₂×C₄×C₈	—	5	1	no	—
277	#335	—	5	1	no	—
278	#335	—	5	1	no	—
279	#335	—	5	1	no	—
280	#335	C₂×D₅	1	1	yes	characteristic, complemented
281	D₄⋊C₈	—	5	1	no	—
282	D₄⋊C₈	—	5	1	no	—
283	D₄⋊C₈	—	5	1	no	—
284	D₄⋊C₈	—	5	1	no	—
285	D₄⋊C₈	—	5	1	no	—
286	D₄⋊C₈	—	5	1	no	—
287	D₄⋊C₈	C₂×D₅	1	1	yes	characteristic, complemented
288	D₄⋊C₈	C₂×D₅	1	1	yes	characteristic, complemented
289	#322	—	5	1	no	—
290	#322	C₂×D₅	1	1	yes	characteristic, complemented
291	C₈²	—	5	1	no	—
292	C₈²	—	5	1	no	—
293	C₂³×C₅	—	2	1	no	—
294	C₂³×C₅	—	2	1	no	—
295	C₂²×D₅	—	2	1	no	—
296	C₂²×D₅	—	2	1	no	—
297	C₂²×D₅	—	4	2	no	—
298	C₂²×D₅	—	4	2	no	—
299	C₂²×D₅	—	4	2	no	—
300	C₂²×D₅	—	4	2	no	—
301	C₂²×D₅	—	8	1	no	—
302	C₂²×D₅	—	8	1	no	—
303	C₂²×D₅	C₄×D₄	1	1	yes	characteristic
304	C₅×D₄	—	2	1	no	—
305	C₅×D₄	—	2	1	no	—
306	C₅×D₄	—	2	1	no	—
307	C₅×D₄	C₂×M₁₆	1	2	yes	complemented
308	C₂×C₄×C₅	—	2	1	no	—
309	C₂×C₄×C₅	—	2	1	no	—
310	C₂×C₄×C₅	—	4	1	no	—
311	C₂×C₄×C₅	—	4	1	no	—
312	C₂×C₄×C₅	—	4	1	no	—
313	C₂×C₄×C₅	—	4	1	no	—
314	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
315	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
316	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
317	C₂²⋊D₅	—	4	2	no	—
318	C₂²⋊D₅	—	4	2	no	—
319	C₂×Dic₅	—	2	1	no	—
320	C₂×Dic₅	—	2	1	no	—
321	C₂×Dic₅	—	4	2	no	—
322	C₂×Dic₅	—	4	2	no	—
323	C₂×Dic₅	C₄×D₄	1	1	yes	characteristic
324	C₂×Dic₅	C₄×D₄	1	1	yes	characteristic
325	C₂×Dic₅	C₄×D₄	1	1	yes	characteristic
326	D₂₀	—	2	1	no	—
327	D₂₀	—	2	1	no	—
328	D₂₀	—	2	1	no	—
329	D₂₀	C₂×M₁₆	1	2	yes	complemented
330	C₄×D₅	—	2	1	no	—
331	C₄×D₅	—	2	1	no	—
332	C₄×D₅	—	4	1	no	—
333	C₄×D₅	—	4	2	no	—
334	C₄×D₅	—	4	2	no	—
335	C₄×D₅	—	4	1	no	—
336	C₄×D₅	—	4	1	no	—
337	C₄×D₅	—	4	1	no	—
338	C₄×D₅	—	4	1	no	—
339	C₄×D₅	—	4	2	no	—
340	C₄×D₅	—	4	2	no	—
341	C₄×D₅	C₂×D₈	1	2	yes	—
342	C₄×D₅	#135	1	2	yes	—
343	C₅×C₈	—	2	1	no	—
344	C₅×C₈	—	2	1	no	—
345	C₅×C₈	—	2	1	no	—
346	C₅×C₈	—	4	1	no	—
347	C₅×C₈	—	4	1	no	—
348	C₅×C₈	—	4	1	no	—
349	C₅×C₈	C₂×D₈	1	2	yes	complemented
350	#168	—	2	1	no	—
351	#168	—	2	1	no	—
352	#168	—	4	1	no	—
353	#168	—	4	1	no	—
354	#168	—	4	1	no	—
355	#168	C₂×M₁₆	1	2	yes	complemented
356	#168	C₂×D₈	1	2	yes	complemented
357	C₂²×D₄	—	5	1	no	—
358	C₂²×D₄	—	5	1	no	—
359	C₂³×C₄	—	10	1	no	—
360	C₂³×C₄	—	10	1	no	—
361	C₂×D₈	—	5	1	no	—
362	C₂×D₈	—	5	1	no	—
363	C₂×D₈	—	5	1	no	—
364	C₂×D₈	—	10	4	no	—
365	C₂×D₈	C₄×D₅	1	1	yes	characteristic
366	C₂×M₁₆	—	2	1	no	—
367	C₂×M₁₆	—	5	1	no	—
368	C₂×M₁₆	—	5	1	no	—
369	C₂×M₁₆	—	10	1	no	—
370	C₂×M₁₆	—	10	1	no	—
371	C₂×M₁₆	—	10	1	no	—
372	C₂×M₁₆	—	10	1	no	—
373	C₂×M₁₆	—	10	1	no	—
374	C₂×M₁₆	—	20	4	no	—
375	C₂×M₁₆	—	20	4	no	—
376	C₂²×C₈	—	2	1	no	—
377	C₂²×C₈	—	5	1	no	—
378	C₂²×C₈	—	5	1	no	—
379	C₂²×C₈	—	10	1	no	—
380	C₂²×C₈	—	10	1	no	—
381	C₂²×C₈	—	10	1	no	—
382	C₄×D₄	—	5	1	no	—
383	C₄×D₄	—	5	1	no	—
384	C₄×D₄	—	5	1	no	—
385	C₄×D₄	—	5	1	no	—
386	C₄×D₄	—	5	1	no	—
387	C₄×D₄	—	5	1	no	—
388	C₄×D₄	—	10	1	no	—
389	C₄×D₄	—	10	1	no	—
390	C₄×D₄	—	10	1	no	—
391	C₄×D₄	—	10	1	no	—
392	C₄×D₄	C₂²×D₅	1	1	yes	characteristic
393	C₄×D₄	C₂²×D₅	1	1	yes	characteristic
394	C₂×C₄⋊C₄	—	5	1	no	—
395	C₂×C₄⋊C₄	—	5	1	no	—
396	C₂×C₂²⋊C₄	—	10	1	no	—
397	C₂×C₂²⋊C₄	—	10	1	no	—
398	C₂×C₄²	—	5	1	no	—
399	#107	—	5	1	no	—
400	#107	—	5	1	no	—
401	#107	—	5	1	no	—
402	#107	C₄×D₅	1	1	yes	characteristic
403	C₄⋊C₈	—	5	1	no	—
404	C₄⋊C₈	—	5	1	no	—
405	C₄⋊C₈	—	10	1	no	—
406	C₄⋊C₈	—	10	1	no	—
407	C₄⋊C₈	—	10	1	no	—
408	C₄⋊C₈	C₂²×D₅	1	1	yes	characteristic
409	C₄⋊C₈	C₂²×D₅	1	1	yes	characteristic
410	#102	—	5	1	no	—
411	#102	—	5	1	no	—
412	#102	—	5	1	no	—
413	#102	—	5	1	no	—
414	#102	—	5	1	no	—
415	#102	—	5	1	no	—
416	#102	C₄×D₅	1	1	yes	characteristic
417	#102	C₄×D₅	1	1	yes	characteristic
418	C₂²⋊C₈	—	2	1	no	—
419	C₂²⋊C₈	—	2	1	no	—
420	C₂²⋊C₈	—	10	1	no	—
421	C₂²⋊C₈	—	10	1	no	—
422	C₂²⋊C₈	—	10	1	no	—
423	C₂²⋊C₈	—	10	1	no	—
424	C₂²⋊C₈	—	10	1	no	—
425	C₂²⋊C₈	—	10	1	no	—
426	C₂²⋊C₈	—	10	1	no	—
427	#97	—	5	1	no	—
428	#97	—	5	1	no	—
429	C₄×C₈	—	5	1	no	—
430	C₄×C₈	—	5	1	no	—
431	C₄×C₈	—	5	1	no	—
432	C₄×C₈	—	5	1	no	—
433	C₄×C₈	—	5	1	no	—
434	C₄×C₈	C₂²×D₅	1	1	yes	characteristic
435	C₄×C₈	C₂²×D₅	1	1	yes	characteristic
436	C₄×C₈	C₂²×D₅	1	1	yes	characteristic
437	C₂²×C₅	—	2	2	no	—
438	C₂²×C₅	—	4	1	no	—
439	C₂²×C₅	—	4	1	no	—
440	C₂²×C₅	—	4	1	no	—
441	C₂²×C₅	—	4	1	no	—
442	C₂²×C₅	—	4	1	no	—
443	C₂²×C₅	C₂×C₄×D₄	1	1	yes	characteristic
444	C₂×D₅	—	2	1	no	—
445	C₂×D₅	—	2	1	no	—
446	C₂×D₅	—	2	2	no	—
447	C₂×D₅	—	4	1	no	—
448	C₂×D₅	—	4	1	no	—
449	C₂×D₅	—	4	1	no	—
450	C₂×D₅	—	4	1	no	—
451	C₂×D₅	—	4	1	no	—
452	C₂×D₅	—	8	4	no	—
453	C₂×D₅	—	8	4	no	—
454	C₂×D₅	C₄×D₈	1	2	yes	—
455	C₄×C₅	—	2	1	no	—
456	C₄×C₅	—	4	1	no	—
457	C₄×C₅	—	4	1	no	—
458	C₄×C₅	C₂²×M₁₆	1	1	yes	characteristic
459	C₄×C₅	#568	1	1	yes	characteristic
460	C₄×C₅	C₂²×D₈	1	1	yes	characteristic
461	C₄×C₅	C₂×#135	1	1	yes	characteristic
462	Dic₅	—	2	1	no	—
463	Dic₅	—	2	1	no	—
464	Dic₅	—	4	1	no	—
465	Dic₅	—	4	1	no	—
466	Dic₅	C₄×D₈	1	2	yes	—
467	C₂⁴	—	10	1	no	—
468	C₂⁴	—	10	1	no	—
469	C₂×D₄	—	5	1	no	—
470	C₂×D₄	—	5	1	no	—
471	C₂×D₄	—	10	1	no	—
472	C₂×D₄	—	10	1	no	—
473	C₂×D₄	—	10	2	no	—
474	C₂×D₄	—	10	2	no	—
475	C₂×D₄	—	20	1	no	—
476	C₂×D₄	—	20	1	no	—
477	C₂×D₄	C₂×C₄×D₅	1	1	yes	characteristic
478	C₂×D₄	C₂×C₄×D₅	1	1	yes	characteristic
479	C₂²×C₄	—	2	1	no	—
480	C₂²×C₄	—	2	1	no	—
481	C₂²×C₄	—	5	1	no	—
482	C₂²×C₄	—	5	1	no	—
483	C₂²×C₄	—	5	1	no	—
484	C₂²×C₄	—	10	1	no	—
485	C₂²×C₄	—	10	1	no	—
486	C₂²×C₄	—	10	1	no	—
487	C₂²×C₄	—	10	1	no	—
488	C₂²×C₄	—	10	1	no	—
489	C₂²×C₄	—	10	1	no	—
490	C₂²×C₄	—	10	1	no	—
491	C₂²×C₄	—	10	1	no	—
492	C₂²×C₄	—	20	2	no	—
493	C₂²×C₄	—	20	2	no	—
494	C₂²×C₄	—	20	2	no	—
495	C₂²×C₄	—	20	2	no	—
496	D₈	—	2	2	no	—
497	D₈	—	5	4	no	—
498	D₈	—	10	2	no	—
499	D₈	—	10	2	no	—
500	M₁₆	—	4	2	no	—
501	M₁₆	—	5	4	no	—
502	M₁₆	—	10	2	no	—
503	M₁₆	—	20	2	no	—
504	M₁₆	—	20	2	no	—
505	M₁₆	—	20	2	no	—
506	M₁₆	—	20	2	no	—
507	M₁₆	—	20	2	no	—
508	C₂×C₈	—	2	1	no	—
509	C₂×C₈	—	2	1	no	—
510	C₂×C₈	—	2	1	no	—
511	C₂×C₈	—	4	2	no	—
512	C₂×C₈	—	5	1	no	—
513	C₂×C₈	—	5	1	no	—
514	C₂×C₈	—	5	1	no	—
515	C₂×C₈	—	5	1	no	—
516	C₂×C₈	—	10	2	no	—
517	C₂×C₈	—	10	1	no	—
518	C₂×C₈	—	10	1	no	—
519	C₂×C₈	—	10	1	no	—
520	C₂×C₈	—	20	1	no	—
521	C₂×C₈	—	20	2	no	—
522	C₂×C₈	—	20	2	no	—
523	C₂×C₈	—	20	2	no	—
524	C₂×C₈	C₂×C₄×D₅	1	1	yes	characteristic
525	C₂×C₈	C₂×C₄×D₅	1	1	yes	characteristic
526	C₂×C₈	D₄×D₅	1	1	yes	characteristic
527	C₂×C₈	D₄×D₅	1	1	yes	characteristic
528	C₄⋊C₄	—	5	1	no	—
529	C₄⋊C₄	—	5	1	no	—
530	C₄⋊C₄	—	10	1	no	—
531	C₄⋊C₄	—	10	1	no	—
532	C₄⋊C₄	C₂×C₄×D₅	1	1	yes	characteristic
533	C₄⋊C₄	C₂×C₄×D₅	1	1	yes	characteristic
534	C₂²⋊C₄	—	2	1	no	—
535	C₂²⋊C₄	—	2	1	no	—
536	C₂²⋊C₄	—	10	1	no	—
537	C₂²⋊C₄	—	10	1	no	—
538	C₂²⋊C₄	—	10	1	no	—
539	C₂²⋊C₄	—	10	1	no	—
540	C₂²⋊C₄	—	10	1	no	—
541	C₂²⋊C₄	—	10	1	no	—
542	C₄²	—	5	1	no	—
543	C₄²	—	5	1	no	—
544	C₄²	—	5	1	no	—
545	C₄²	C₂³×D₅	1	1	yes	characteristic
546	C₂×C₅	—	4	2	no	—
547	C₂×C₅	—	8	1	no	—
548	C₂×C₅	D₄×M₁₆	1	1	yes	characteristic
549	C₂×C₅	C₂×C₄×D₈	1	1	yes	characteristic
550	C₂×C₅	#2957	1	1	yes	characteristic
551	D₅	—	2	2	no	—
552	D₅	—	4	2	no	—
553	D₅	—	8	1	no	—
554	C₂³	—	2	1	no	—
555	C₂³	—	2	1	no	—
556	C₂³	—	5	1	no	—
557	C₂³	—	10	1	no	—
558	C₂³	—	10	1	no	—
559	C₂³	—	20	2	no	—
560	C₂³	—	20	2	no	—
561	C₂³	—	20	2	no	—
562	C₂³	—	20	2	no	—
563	C₂³	—	40	1	no	—
564	C₂³	—	40	1	no	—
565	D₄	—	2	1	no	—
566	D₄	—	2	1	no	—
567	D₄	—	2	1	no	—
568	D₄	—	5	2	no	—
569	D₄	—	10	1	no	—
570	D₄	—	10	1	no	—
571	D₄	—	10	1	no	—
572	D₄	—	20	2	no	—
573	D₄	—	20	2	no	—
574	D₄	D₅×M₁₆	1	2	yes	complemented
575	C₂×C₄	—	2	1	no	—
576	C₂×C₄	—	2	1	no	—
577	C₂×C₄	—	4	1	no	—
578	C₂×C₄	—	4	1	no	—
579	C₂×C₄	—	4	1	no	—
580	C₂×C₄	—	4	1	no	—
581	C₂×C₄	—	5	1	no	—
582	C₂×C₄	—	5	2	no	—
583	C₂×C₄	—	5	2	no	—
584	C₂×C₄	—	5	1	no	—
585	C₂×C₄	—	5	1	no	—
586	C₂×C₄	—	10	1	no	—
587	C₂×C₄	—	10	1	no	—
588	C₂×C₄	—	10	1	no	—
589	C₂×C₄	—	10	1	no	—
590	C₂×C₄	—	20	1	no	—
591	C₂×C₄	—	20	2	no	—
592	C₂×C₄	—	20	2	no	—
593	C₂×C₄	—	20	2	no	—
594	C₂×C₄	—	20	2	no	—
595	C₂×C₄	—	20	2	no	—
596	C₂×C₄	—	20	2	no	—
597	C₂×C₄	—	20	1	no	—
598	C₂×C₄	—	20	1	no	—
599	C₂×C₄	—	20	1	no	—
600	C₂×C₄	—	20	1	no	—
601	C₂×C₄	C₂²×C₄×D₅	1	1	yes	characteristic
602	C₂×C₄	C₂×D₄×D₅	1	1	yes	characteristic
603	C₂×C₄	D₅×#41	1	1	yes	characteristic
604	C₈	—	2	1	no	—
605	C₈	—	2	1	no	—
606	C₈	—	2	1	no	—
607	C₈	—	4	1	no	—
608	C₈	—	4	1	no	—
609	C₈	—	4	1	no	—
610	C₈	—	5	2	no	—
611	C₈	—	5	2	no	—
612	C₈	—	10	1	no	—
613	C₈	—	10	1	no	—
614	C₈	—	20	1	no	—
615	C₈	—	20	1	no	—
616	C₈	—	20	1	no	—
617	C₈	D₅×D₈	1	2	yes	complemented
618	C₅	M₁₆×D₈	1	1	yes	characteristic, complemented, Sylow
619	C₂²	—	2	2	no	—
620	C₂²	—	4	1	no	—
621	C₂²	—	4	1	no	—
622	C₂²	—	4	1	no	—
623	C₂²	—	4	1	no	—
624	C₂²	—	4	1	no	—
625	C₂²	—	5	2	no	—
626	C₂²	—	10	1	no	—
627	C₂²	—	10	1	no	—
628	C₂²	—	10	2	no	—
629	C₂²	—	20	1	no	—
630	C₂²	—	20	1	no	—
631	C₂²	—	20	1	no	—
632	C₂²	—	20	1	no	—
633	C₂²	—	20	1	no	—
634	C₂²	—	40	4	no	—
635	C₂²	—	40	4	no	—
636	C₂²	C₄×D₄×D₅	1	1	yes	characteristic
637	C₄	—	2	1	no	—
638	C₄	—	4	1	no	—
639	C₄	—	4	1	no	—
640	C₄	—	5	2	no	—
641	C₄	—	10	1	no	—
642	C₄	—	10	1	no	—
643	C₄	—	20	1	no	—
644	C₄	—	20	1	no	—
645	C₄	C₂×D₅×M₁₆	1	1	yes	characteristic
646	C₄	#66084	1	1	yes	characteristic
647	C₄	C₂×D₅×D₈	1	1	yes	characteristic
648	C₄	D₅×#135	1	1	yes	characteristic
649	C₂	—	4	2	no	—
650	C₂	—	8	1	no	—
651	C₂	—	10	2	no	—
652	C₂	—	20	2	no	—
653	C₂	—	40	1	no	—
654	C₂	#10611214	1	1	yes	characteristic
655	C₂	C₄×D₅×D₈	1	1	yes	characteristic
656	C₂	#10611630	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	C₂×D₅×D₈	C₄
cosocle	C₄²×C₅	C₂⁴
hypercenter	#1581	D₅
hypocenter	C₅	M₁₆×D₈
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. #10611271	C₂	semidirect
3. D₄×#676	C₂	semidirect
4. C₅×#1581	C₂	semidirect
5. #10601672	C₂	semidirect
6. #10601652	C₂	semidirect
7. C₈×#686	C₂	semidirect
8. #10599362	C₂	semidirect
9. #10599352	C₂	semidirect
10. #10598965	C₂	semidirect
11. #10598965	C₂	semidirect
12. #10598953	C₂	semidirect
13. #10598941	C₂	semidirect
14. #10598871	C₂	semidirect
15. #10598860	C₂	semidirect
22. C₅×#436	C₂²	semidirect
23. C₅×C₈×D₄	C₂²	semidirect
29. #65301	C₂²	semidirect
30. D₄×#168	C₂²	semidirect
33. #65127	C₂²	semidirect
36. #65123	C₂²	semidirect
46. #64977	C₂²	semidirect
48. C₈×D₂₀	C₂²	semidirect
51. C₅×#335	C₂²	semidirect
52. C₅×D₄⋊C₈	C₂²	semidirect
53. C₅×D₄⋊C₈	C₂²	semidirect
54. C₅×#322	C₂²	semidirect
55. D₄⋊#168	C₂²	semidirect
56. D₄⋊#168	C₂²	semidirect
57. #64703	C₂²	semidirect
58. #64703	C₂²	semidirect
59. #64699	C₂²	semidirect
60. #64699	C₂²	semidirect
61. #64679	C₂²	semidirect
62. #64679	C₂²	semidirect
63. #64678	C₂²	semidirect
64. #64674	C₂²	semidirect
65. C₈×#168	C₂²	semidirect
66. C₈×#168	C₂²	semidirect
156. #1581	D₅	semidirect
210. #686	M₁₆	semidirect
237. #676	D₈	semidirect
258. #436	C₂×D₅	semidirect
266. C₈×D₄	C₂×D₅	semidirect
280. #335	C₂×D₅	semidirect
287. D₄⋊C₈	C₂×D₅	semidirect
288. D₄⋊C₈	C₂×D₅	semidirect
290. #322	C₂×D₅	semidirect
307. C₅×D₄	C₂×M₁₆	semidirect
329. D₂₀	C₂×M₁₆	semidirect
349. C₅×C₈	C₂×D₈	semidirect
355. #168	C₂×M₁₆	semidirect
356. #168	C₂×D₈	semidirect
574. D₄	D₅×M₁₆	semidirect
617. C₈	D₅×D₈	semidirect
618. C₅	M₁₆×D₈	semidirect

Maximal subgroups

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

subgroup	index
C₄×D₅×D₈	2
#10611271	2
D₄×#676	2
C₅×#1581	2
#10601672	2
#10601652	2
C₈×#686	2
#10599362	2
#10599352	2
#10598965	2
#10598953	2
#10598941	2
#10598871	2
#10598860	2
M₁₆×D₈	5