Subgroups — #14418501

Order 1920.

728 conjugacy classes of subgroups.

The subgroup lattice has 644 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11752578	C₂	1	1	yes	maximal, characteristic
2	C₈×Dic₃₀	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#4689	C₂	1	1	yes	maximal, characteristic
4	C₃×C₈×Dic₁₀	C₂	1	1	yes	maximal, characteristic, complemented
5	#11747827	C₂	1	1	yes	maximal, characteristic, complemented
6	C₈×#1204	C₂	1	1	yes	maximal, characteristic, complemented
7	C₈×#1204	C₂	1	1	yes	maximal, characteristic, complemented
8	#11747661	C₂	1	1	yes	maximal, characteristic
9	#11747653	C₂	1	1	yes	maximal, characteristic
10	#11747590	C₂	1	1	yes	maximal, characteristic
11	D₃×C₈×Dic₅	C₂	1	1	yes	maximal, characteristic
12	#11747567	C₂	1	1	yes	maximal, characteristic, complemented
13	#11746993	C₂	1	1	yes	maximal, characteristic
14	#11746856	C₂	1	1	yes	maximal, characteristic, complemented
15	#11746847	C₂	1	1	yes	maximal, characteristic, complemented
16	#10610273	—	3	1	no	maximal, Hall
17	C₄×Dic₃₀	C₂²	1	1	yes	characteristic
18	C₂×C₅×ΓL(1,𝔽₂₅)	C₂²	1	1	yes	characteristic
19	C₂×C₅×D₃×C₈	C₂²	1	1	yes	characteristic
20	C₅×#872	C₂²	1	1	yes	characteristic
21	C₃×C₄×Dic₁₀	C₂²	1	1	yes	characteristic
22	C₄×#1204	C₂²	1	1	yes	characteristic
23	C₄×#1204	C₂²	1	1	yes	characteristic
24	#91436	C₄	1	1	yes	characteristic
25	#91432	C₄	1	1	yes	characteristic
26	#91417	C₄	1	1	yes	characteristic
27	#91410	C₄	1	1	yes	characteristic
28	C₄×D₃×Dic₅	C₂²	1	1	yes	characteristic
29	#91371	C₂²	1	1	yes	characteristic
30	#91346	C₄	1	1	yes	characteristic
31	#91343	C₄	1	1	yes	characteristic
32	#91328	C₄	1	1	yes	characteristic
33	#91327	C₄	1	1	yes	characteristic
34	C₂×#6650	C₂²	1	1	yes	characteristic
35	C₂×D₃×#168	C₂²	1	1	yes	characteristic
36	C₃×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
37	#91098	C₂²	1	1	yes	characteristic
38	#91098	C₂²	1	1	yes	characteristic
39	C₈×Dic₁₅	C₂²	1	1	yes	characteristic
40	C₈×Dic₁₅	C₂²	1	1	yes	characteristic
41	C₄⋊(C₃⋊#168)	C₂²	1	1	yes	characteristic
42	C₅×#815	C₂²	1	1	yes	characteristic
43	C₅×C₈×Dic₃	C₂²	1	1	yes	characteristic
44	C₅×#803	C₂²	1	1	yes	characteristic
45	C₃×#3946	C₂²	1	1	yes	characteristic
46	C₃×#3946	C₂²	1	1	yes	characteristic
47	C₃×C₈×Dic₅	C₂²	1	1	yes	characteristic
48	C₃×C₈×Dic₅	C₂²	1	1	yes	characteristic
49	C₃×C₄⋊#168	C₂²	1	1	yes	characteristic
50	Dic₃⋊#168	C₂²	1	1	yes	characteristic
51	Dic₃⋊#168	C₂²	1	1	yes	characteristic
52	#90983	C₂²	1	1	yes	characteristic
53	#90983	C₂²	1	1	yes	characteristic
54	#90982	C₂²	1	1	yes	characteristic
55	#90982	C₂²	1	1	yes	characteristic
56	#90954	C₂²	1	1	yes	characteristic
57	#90952	C₂²	1	1	yes	characteristic
58	#90951	C₂²	1	1	yes	characteristic
59	Dic₅×C₃⋊C₈	C₂²	1	1	yes	characteristic
60	#79917	—	5	1	no	maximal, Hall
61	#65851	—	3	1	no	—
62	C₅×#405	—	3	1	no	—
63	#65408	—	3	1	no	—
64	#65407	—	3	1	no	—
65	#65390	—	3	1	no	—
66	C₂×C₈×Dic₅	—	3	1	no	—
67	#65288	—	3	1	no	—
68	#64990	—	3	1	no	—
69	#64990	—	3	1	no	—
70	#64990	—	3	1	no	—
71	#64990	—	3	1	no	—
72	C₈×Dic₁₀	—	3	1	no	—
73	C₈×Dic₁₀	—	3	1	no	—
74	C₈×Dic₁₀	—	3	1	no	—
75	C₈×Dic₁₀	D₃	1	1	yes	characteristic, complemented
76	C₂×Dic₃₀	C₂×C₄	1	1	yes	characteristic
77	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
78	C₂×C₃×Dic₁₀	C₂×C₄	1	1	yes	characteristic
79	C₂×#1204	C₂×C₄	1	1	yes	characteristic
80	C₂×#1204	C₂×C₄	1	1	yes	characteristic
81	C₂×D₃×Dic₅	C₂×C₄	1	1	yes	characteristic
82	C₂×D₃×Dic₅	C₂×C₄	1	1	yes	characteristic
83	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
84	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
85	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
86	C₄⋊Dic₁₅	C₂×C₄	1	1	yes	characteristic
87	#6712	C₂×C₄	1	1	yes	characteristic
88	#6712	C₂×C₄	1	1	yes	characteristic
89	C₄×Dic₁₅	C₂³	1	1	yes	characteristic
90	C₄×Dic₁₅	C₂³	1	1	yes	characteristic
91	C₂×C₃⋊#168	C₂³	1	1	yes	characteristic
92	C₂×C₃⋊#168	C₂³	1	1	yes	characteristic
93	C₅×(C₂×D₃)⋊C₄	C₂×C₄	1	1	yes	characteristic
94	C₅×(C₂×D₃)⋊C₄	C₂×C₄	1	1	yes	characteristic
95	C₅×Dic₃⋊C₄	C₂×C₄	1	1	yes	characteristic
96	C₅×Dic₃⋊C₄	C₂×C₄	1	1	yes	characteristic
97	C₄×C₅×Dic₃	C₂³	1	1	yes	characteristic
98	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
99	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
100	C₅×ΓL(1,𝔽₂₅)	—	2	2	no	—
101	C₅×D₃×C₈	Q₈	1	4	yes	complemented
102	C₃×C₄⋊Dic₅	C₂×C₄	1	1	yes	characteristic
103	C₃×#683	C₂×C₄	1	1	yes	characteristic
104	C₃×#683	C₂×C₄	1	1	yes	characteristic
105	C₃×C₄×Dic₅	C₂³	1	1	yes	characteristic
106	C₃×C₄×Dic₅	C₂³	1	1	yes	characteristic
107	C₂×C₃×#168	C₂³	1	1	yes	characteristic
108	C₂×C₃×#168	C₂³	1	1	yes	characteristic
109	Dic₃⋊Dic₅	C₂×C₄	1	1	yes	characteristic
110	Dic₃⋊Dic₅	C₂×C₄	1	1	yes	characteristic
111	Dic₃⋊Dic₅	C₂×C₄	1	1	yes	characteristic
112	Dic₃⋊Dic₅	C₂×C₄	1	1	yes	characteristic
113	#6669	C₂×C₄	1	1	yes	characteristic
114	#6669	C₂×C₄	1	1	yes	characteristic
115	#6668	C₂×C₄	1	1	yes	characteristic
116	#6668	C₂×C₄	1	1	yes	characteristic
117	(C₂×D₃)⋊Dic₅	C₂×C₄	1	1	yes	characteristic
118	(C₂×D₃)⋊Dic₅	C₂×C₄	1	1	yes	characteristic
119	Dic₃×Dic₅	C₂×C₄	1	1	yes	characteristic
120	Dic₃×Dic₅	C₂×C₄	1	1	yes	characteristic
121	#6650	—	2	2	no	—
122	D₃×#168	—	2	2	no	—
123	#5578	—	5	1	no	—
124	C₃×C₈×Q₈	—	5	1	no	—
125	#5024	—	5	1	no	—
126	#4839	—	5	1	no	—
127	#4839	—	5	1	no	—
128	#4837	—	5	1	no	—
129	#4831	—	5	1	no	—
130	#4828	—	5	1	no	—
131	#4828	—	5	1	no	—
132	#4689	—	5	1	no	—
133	#4689	D₅	1	1	yes	characteristic
134	C₄×D₃×C₈	—	5	1	no	—
135	C₈×Dic₆	—	5	1	no	—
136	C₈×Dic₆	—	5	1	no	—
137	C₈×Dic₆	—	5	1	no	—
138	C₂×C₅×M₁₆	—	3	1	no	—
139	C₂²×C₅×C₈	—	3	1	no	—
140	C₅×#117	—	3	1	no	—
141	#4072	—	3	1	no	—
142	C₂×C₄×Dic₅	—	3	1	no	—
143	C₂×#681	—	3	1	no	—
144	C₂²×#168	—	3	1	no	—
145	#4036	—	3	1	no	—
146	#4036	—	3	1	no	—
147	#4034	—	3	1	no	—
148	#4034	—	3	1	no	—
149	#4024	—	3	1	no	—
150	#4024	—	3	1	no	—
151	#4024	—	3	1	no	—
152	#4024	—	3	1	no	—
153	C₄×Dic₁₀	—	3	1	no	—
154	C₄×Dic₁₀	—	3	1	no	—
155	C₄×Dic₁₀	—	3	1	no	—
156	C₄×Dic₁₀	C₂×D₃	1	1	yes	characteristic
157	C₅×#97	—	3	1	no	—
158	C₅×#97	—	3	1	no	—
159	C₄×C₅×C₈	—	3	1	no	—
160	C₄×C₅×C₈	C₂×D₃	1	1	yes	characteristic
161	#3947	—	3	1	no	—
162	#3947	—	3	1	no	—
163	#3946	—	3	1	no	—
164	#3946	—	3	1	no	—
165	#3946	—	3	1	no	—
166	#3946	—	3	1	no	—
167	#3946	—	3	1	no	—
168	#3946	—	3	1	no	—
169	#3946	C₂×D₃	1	1	yes	characteristic
170	#3946	C₂×D₃	1	1	yes	characteristic
171	C₈×Dic₅	—	3	1	no	—
172	C₈×Dic₅	—	3	1	no	—
173	C₈×Dic₅	—	3	1	no	—
174	C₈×Dic₅	—	3	1	no	—
175	C₈×Dic₅	C₂×D₃	1	1	yes	characteristic
176	C₈×Dic₅	C₂×D₃	1	1	yes	characteristic
177	C₄⋊#168	—	3	1	no	—
178	C₄⋊#168	—	3	1	no	—
179	C₄⋊#168	—	3	1	no	—
180	C₄⋊#168	C₂×D₃	1	1	yes	characteristic
181	#2960	—	15	1	no	Sylow
182	C₂²×C₅×D₃	C₂²×C₄	1	1	yes	characteristic
183	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
184	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
185	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
186	C₂×Dic₁₅	C₂²×C₄	1	1	yes	characteristic
187	C₂×Dic₁₅	C₂²×C₄	1	1	yes	characteristic
188	C₂×Dic₁₅	C₂²×C₄	1	1	yes	characteristic
189	C₂×Dic₁₅	C₂²×C₄	1	1	yes	characteristic
190	Dic₃₀	—	2	2	no	—
191	C₂×C₅×Dic₃	C₂²×C₄	1	1	yes	characteristic
192	C₂×C₅×Dic₃	C₂²×C₄	1	1	yes	characteristic
193	C₂×C₅×Dic₃	C₂²×C₄	1	1	yes	characteristic
194	C₄×C₅×D₃	C₂×Q₈	1	2	yes	—
195	C₄×C₅×D₃	#41	1	2	yes	—
196	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
197	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
198	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
199	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
200	C₃×Dic₁₀	—	2	2	no	—
201	#1204	—	2	2	no	—
202	#1204	—	2	2	no	—
203	D₃×Dic₅	—	2	2	no	—
204	D₃×Dic₅	—	2	2	no	—
205	C₃×C₅×C₈	—	2	1	no	—
206	C₃×C₅×C₈	C₂×Q₈	1	2	yes	—
207	C₃⋊#168	—	2	1	no	—
208	C₃⋊#168	—	2	1	no	—
209	C₃×#168	—	2	1	no	—
210	C₃×#168	—	2	1	no	—
211	C₅×C₃⋊C₈	—	2	1	no	—
212	C₅×C₃⋊C₈	C₂×Q₈	1	2	yes	—
213	C₃×C₄×Q₈	—	5	1	no	—
214	#946	—	5	1	no	—
215	#944	—	5	1	no	—
216	C₂×ΓL(1,𝔽₂₅)	—	5	1	no	—
217	C₂×ΓL(1,𝔽₂₅)	C₂×D₅	1	1	yes	characteristic
218	C₂×D₃×C₈	—	5	1	no	—
219	C₂×D₃×C₈	C₂×D₅	1	1	yes	characteristic
220	#897	—	5	1	no	—
221	#896	—	5	1	no	—
222	#896	—	5	1	no	—
223	#889	—	5	1	no	—
224	#889	—	5	1	no	—
225	#888	—	5	1	no	—
226	#872	—	5	1	no	—
227	#872	C₂×D₅	1	1	yes	characteristic
228	C₄²×D₃	—	5	1	no	—
229	C₄×Dic₆	—	5	1	no	—
230	C₄×Dic₆	—	5	1	no	—
231	C₄×Dic₆	—	5	1	no	—
232	C₃×C₄⋊C₈	—	5	1	no	—
233	C₃×C₄⋊C₈	—	5	1	no	—
234	C₃×C₄⋊C₈	—	5	1	no	—
235	C₃×C₄×C₈	—	5	1	no	—
236	C₃×C₄×C₈	—	5	1	no	—
237	C₃×C₄×C₈	C₂×D₅	1	1	yes	characteristic
238	#815	—	5	1	no	—
239	#815	C₂×D₅	1	1	yes	characteristic
240	Dic₃⋊C₈	—	5	1	no	—
241	Dic₃⋊C₈	—	5	1	no	—
242	Dic₃⋊C₈	—	5	1	no	—
243	Dic₃⋊C₈	—	5	1	no	—
244	Dic₃⋊C₈	—	5	1	no	—
245	Dic₃⋊C₈	—	5	1	no	—
246	C₈×Dic₃	—	5	1	no	—
247	C₈×Dic₃	—	5	1	no	—
248	C₈×Dic₃	—	5	1	no	—
249	C₈×Dic₃	C₂×D₅	1	1	yes	characteristic
250	C₄⋊(C₃⋊C₈)	—	5	1	no	—
251	C₄⋊(C₃⋊C₈)	—	5	1	no	—
252	C₄⋊(C₃⋊C₈)	—	5	1	no	—
253	#803	—	5	1	no	—
254	#803	C₂×D₅	1	1	yes	characteristic
255	C₄×C₃⋊C₈	—	5	1	no	—
256	C₂²×C₄×C₅	—	3	1	no	—
257	C₂²×Dic₅	—	3	1	no	—
258	C₂²×Dic₅	—	3	1	no	—
259	C₂×Dic₁₀	—	3	1	no	—
260	C₂×Dic₁₀	—	3	1	no	—
261	C₂×Dic₁₀	—	3	1	no	—
262	C₂×Dic₁₀	C₄×D₃	1	1	yes	characteristic
263	C₅×M₁₆	—	6	2	no	—
264	C₂×C₅×C₈	—	3	1	no	—
265	C₂×C₅×C₈	—	3	4	no	—
266	C₂×C₅×C₈	—	3	1	no	—
267	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
268	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
269	C₅×C₄⋊C₄	—	3	1	no	—
270	C₅×C₄⋊C₄	—	3	1	no	—
271	C₅×C₂²⋊C₄	—	3	1	no	—
272	C₅×C₂²⋊C₄	—	3	1	no	—
273	C₄²×C₅	—	3	1	no	—
274	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
275	C₂²⋊Dic₅	—	3	1	no	—
276	C₂²⋊Dic₅	—	3	1	no	—
277	C₄⋊Dic₅	—	3	1	no	—
278	C₄⋊Dic₅	—	3	1	no	—
279	C₄⋊Dic₅	—	3	1	no	—
280	C₄⋊Dic₅	—	3	1	no	—
281	C₄⋊Dic₅	—	3	1	no	—
282	C₄⋊Dic₅	C₄×D₃	1	1	yes	characteristic
283	#683	—	3	1	no	—
284	#683	—	3	1	no	—
285	#683	—	3	1	no	—
286	#683	—	3	1	no	—
287	#683	—	3	1	no	—
288	#683	—	3	1	no	—
289	#683	C₄×D₃	1	1	yes	characteristic
290	#683	C₄×D₃	1	1	yes	characteristic
291	C₄×Dic₅	—	3	1	no	—
292	C₄×Dic₅	—	3	1	no	—
293	C₄×Dic₅	—	3	1	no	—
294	C₄×Dic₅	—	3	1	no	—
295	C₄×Dic₅	C₂²×D₃	1	1	yes	characteristic
296	C₄×Dic₅	C₂²×D₃	1	1	yes	characteristic
297	#681	—	6	2	no	—
298	C₂×#168	—	3	1	no	—
299	C₂×#168	—	3	1	no	—
300	C₂×#168	—	6	2	no	—
301	C₂×#168	C₂²×D₃	1	1	yes	characteristic
302	C₂×#168	C₂²×D₃	1	1	yes	characteristic
303	#533	—	15	1	no	—
304	#446	—	15	1	no	—
305	#446	—	15	1	no	—
306	#446	—	15	1	no	—
307	#446	—	15	1	no	—
308	C₈×Q₈	—	5	1	no	—
309	C₈×Q₈	—	15	1	no	—
310	C₈×Q₈	—	15	1	no	—
311	C₈×Q₈	—	15	1	no	—
312	#424	—	15	1	no	—
313	#424	—	15	1	no	—
314	#423	—	15	1	no	—
315	#405	—	3	1	no	—
316	#405	—	15	1	no	—
317	C₂×C₄×C₈	—	15	1	no	—
318	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
319	C₂×C₅×D₃	—	2	1	no	—
320	C₂×C₅×D₃	—	2	1	no	—
321	C₂×C₅×D₃	C₄×Q₈	1	2	yes	—
322	C₃×C₄×C₅	—	2	1	no	—
323	C₃×C₄×C₅	—	2	1	no	—
324	C₃×C₄×C₅	C₂²×Q₈	1	1	yes	characteristic
325	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
326	Dic₁₅	—	2	1	no	—
327	Dic₁₅	—	2	1	no	—
328	Dic₁₅	—	2	1	no	—
329	Dic₁₅	#131	1	2	yes	—
330	C₃×Dic₅	—	2	1	no	—
331	C₃×Dic₅	—	2	1	no	—
332	C₃×Dic₅	—	2	1	no	—
333	C₃×Dic₅	#131	1	2	yes	—
334	C₅×Dic₃	—	2	1	no	—
335	C₅×Dic₃	—	2	1	no	—
336	C₅×Dic₃	C₄×Q₈	1	2	yes	—
337	C₂×C₃×Q₈	—	5	1	no	—
338	C₂×C₄×D₃	—	5	1	no	—
339	C₂×C₄×D₃	—	5	1	no	—
340	C₂×C₄×D₃	C₂²×D₅	1	1	yes	characteristic
341	C₂×Dic₆	—	5	1	no	—
342	C₂×Dic₆	—	5	1	no	—
343	C₂×Dic₆	—	5	1	no	—
344	C₂×C₃×C₈	—	5	1	no	—
345	C₂×C₃×C₈	—	5	1	no	—
346	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
347	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
348	C₃×C₄⋊C₄	—	5	1	no	—
349	C₃×C₄⋊C₄	—	5	1	no	—
350	C₃×C₄⋊C₄	—	5	1	no	—
351	C₃×C₄²	—	5	1	no	—
352	C₃×C₄²	—	5	1	no	—
353	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
354	(C₂×D₃)⋊C₄	—	5	1	no	—
355	(C₂×D₃)⋊C₄	—	5	1	no	—
356	(C₂×D₃)⋊C₄	C₄×D₅	1	1	yes	characteristic
357	(C₂×D₃)⋊C₄	C₄×D₅	1	1	yes	characteristic
358	C₄⋊Dic₃	—	5	1	no	—
359	C₄⋊Dic₃	—	5	1	no	—
360	C₄⋊Dic₃	—	5	1	no	—
361	Dic₃⋊C₄	—	5	1	no	—
362	Dic₃⋊C₄	—	5	1	no	—
363	Dic₃⋊C₄	—	5	1	no	—
364	Dic₃⋊C₄	—	5	1	no	—
365	Dic₃⋊C₄	—	5	1	no	—
366	Dic₃⋊C₄	—	5	1	no	—
367	Dic₃⋊C₄	—	5	1	no	—
368	Dic₃⋊C₄	—	5	1	no	—
369	Dic₃⋊C₄	C₄×D₅	1	1	yes	characteristic
370	Dic₃⋊C₄	C₄×D₅	1	1	yes	characteristic
371	C₄×Dic₃	—	5	1	no	—
372	C₄×Dic₃	—	5	1	no	—
373	C₄×Dic₃	—	5	1	no	—
374	C₄×Dic₃	—	5	1	no	—
375	C₄×Dic₃	C₂²×D₅	1	1	yes	characteristic
376	C₂×C₃⋊C₈	—	5	1	no	—
377	C₂×C₃⋊C₈	—	5	1	no	—
378	C₂×C₃⋊C₈	C₂²×D₅	1	1	yes	characteristic
379	C₂×C₃⋊C₈	C₂²×D₅	1	1	yes	characteristic
380	ΓL(1,𝔽₂₅)	—	2	2	no	—
381	ΓL(1,𝔽₂₅)	—	10	2	no	—
382	D₃×C₈	—	10	2	no	—
383	D₃×C₈	Dic₁₀	1	4	yes	complemented
384	C₂³×C₅	—	3	1	no	—
385	C₂×C₄×C₅	—	3	1	no	—
386	C₂×C₄×C₅	—	3	2	no	—
387	C₂×C₄×C₅	—	3	2	no	—
388	C₂×C₄×C₅	—	3	1	no	—
389	C₂×C₄×C₅	—	3	1	no	—
390	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
391	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
392	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
393	C₂×Dic₅	—	3	1	no	—
394	C₂×Dic₅	—	3	1	no	—
395	C₂×Dic₅	—	3	1	no	—
396	C₂×Dic₅	—	3	1	no	—
397	C₂×Dic₅	—	6	2	no	—
398	C₂×Dic₅	—	6	2	no	—
399	C₂×Dic₅	C₂×C₄×D₃	1	1	yes	characteristic
400	C₂×Dic₅	C₂×C₄×D₃	1	1	yes	characteristic
401	C₂×Dic₅	C₂×C₄×D₃	1	1	yes	characteristic
402	C₂×Dic₅	C₂×C₄×D₃	1	1	yes	characteristic
403	Dic₁₀	—	2	2	no	—
404	Dic₁₀	—	6	2	no	—
405	Dic₁₀	—	6	2	no	—
406	Dic₁₀	—	6	2	no	—
407	C₅×C₈	—	2	1	no	—
408	C₅×C₈	—	3	2	no	—
409	C₅×C₈	—	6	1	no	—
410	C₅×C₈	D₃×Q₈	1	2	yes	—
411	#168	—	2	1	no	—
412	#168	—	2	1	no	—
413	#168	—	6	1	no	—
414	#168	—	6	1	no	—
415	C₂×M₁₆	—	3	1	no	—
416	C₂×M₁₆	—	15	1	no	—
417	C₂²×C₈	—	3	1	no	—
418	C₂²×C₈	—	15	1	no	—
419	C₄⋊Q₈	—	15	1	no	—
420	C₄⋊Q₈	—	15	1	no	—
421	#125	—	15	1	no	—
422	#125	—	15	1	no	—
423	C₂²⋊Q₈	—	15	1	no	—
424	C₂²⋊Q₈	—	15	1	no	—
425	C₂²⋊Q₈	—	15	1	no	—
426	C₂²⋊Q₈	—	15	1	no	—
427	C₄×Q₈	—	5	1	no	—
428	C₄×Q₈	—	15	1	no	—
429	C₄×Q₈	—	15	1	no	—
430	C₄×Q₈	—	15	1	no	—
431	#117	—	3	1	no	—
432	#117	—	15	1	no	—
433	C₂×C₄²	—	15	1	no	—
434	C₄⋊C₈	—	5	1	no	—
435	C₄⋊C₈	—	5	1	no	—
436	C₄⋊C₈	—	5	1	no	—
437	C₄⋊C₈	—	15	1	no	—
438	C₄⋊C₈	—	15	1	no	—
439	C₄⋊C₈	—	15	1	no	—
440	C₄⋊C₈	—	15	1	no	—
441	C₄⋊C₈	—	15	1	no	—
442	C₄⋊C₈	—	15	1	no	—
443	C₄⋊C₈	—	15	1	no	—
444	C₄⋊C₈	—	15	1	no	—
445	C₄⋊C₈	—	15	1	no	—
446	#97	—	3	1	no	—
447	#97	—	3	1	no	—
448	#97	—	15	1	no	—
449	#97	—	15	1	no	—
450	C₄×C₈	—	3	1	no	—
451	C₄×C₈	—	5	1	no	—
452	C₄×C₈	—	5	1	no	—
453	C₄×C₈	—	15	1	no	—
454	C₄×C₈	—	15	1	no	—
455	C₄×C₈	—	15	1	no	—
456	C₄×C₈	—	15	1	no	—
457	C₄×C₈	D₃×D₅	1	1	yes	characteristic
458	C₂×C₃×C₅	C₂×C₄×Q₈	1	1	yes	characteristic
459	C₂×C₃×C₅	C₂×#131	1	1	yes	characteristic
460	C₂×C₃×C₅	C₂×#131	1	1	yes	characteristic
461	C₅×D₃	—	2	2	no	—
462	C₂²×D₃	C₂×C₄×D₅	1	1	yes	characteristic
463	C₃×Q₈	—	10	2	no	—
464	C₂×C₃×C₄	—	5	1	no	—
465	C₂×C₃×C₄	—	5	1	no	—
466	C₂×C₃×C₄	—	5	1	no	—
467	C₂×C₃×C₄	—	5	1	no	—
468	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
469	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
470	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
471	C₂×Dic₃	—	5	1	no	—
472	C₂×Dic₃	—	5	1	no	—
473	C₂×Dic₃	—	5	1	no	—
474	C₂×Dic₃	—	5	1	no	—
475	C₂×Dic₃	C₂×C₄×D₅	1	1	yes	characteristic
476	C₂×Dic₃	C₂×C₄×D₅	1	1	yes	characteristic
477	C₂×Dic₃	C₂×C₄×D₅	1	1	yes	characteristic
478	C₄×D₃	—	10	2	no	—
479	C₄×D₃	—	10	2	no	—
480	C₄×D₃	C₂×Dic₁₀	1	2	yes	—
481	C₄×D₃	#709	1	2	yes	—
482	Dic₆	—	10	2	no	—
483	Dic₆	—	10	2	no	—
484	Dic₆	—	10	2	no	—
485	C₃×C₈	—	2	1	no	—
486	C₃×C₈	—	10	1	no	—
487	C₃×C₈	—	10	1	no	—
488	C₃×C₈	C₂×Dic₁₀	1	2	yes	—
489	C₃⋊C₈	—	2	1	no	—
490	C₃⋊C₈	—	10	1	no	—
491	C₃⋊C₈	—	10	1	no	—
492	C₃⋊C₈	C₂×Dic₁₀	1	2	yes	—
493	C₂²×C₅	—	3	2	no	—
494	C₂²×C₅	—	6	1	no	—
495	C₂²×C₅	—	6	1	no	—
496	C₂²×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
497	C₄×C₅	—	2	1	no	—
498	C₄×C₅	—	2	1	no	—
499	C₄×C₅	—	3	2	no	—
500	C₄×C₅	—	6	1	no	—
501	C₄×C₅	—	6	1	no	—
502	C₄×C₅	C₂×D₃×Q₈	1	1	yes	characteristic
503	C₄×C₅	D₃×#41	1	1	yes	characteristic
504	Dic₅	—	2	1	no	—
505	Dic₅	—	2	1	no	—
506	Dic₅	—	2	1	no	—
507	Dic₅	—	3	2	no	—
508	Dic₅	—	6	1	no	—
509	Dic₅	—	6	1	no	—
510	Dic₅	—	6	1	no	—
511	Dic₅	#901	1	2	yes	—
512	C₂×Q₈	—	5	1	no	—
513	C₂×Q₈	—	15	1	no	—
514	C₂×Q₈	—	15	1	no	—
515	C₂×Q₈	—	15	1	no	—
516	C₂²×C₄	—	3	1	no	—
517	C₂²×C₄	—	15	1	no	—
518	C₂²×C₄	—	15	1	no	—
519	M₁₆	—	6	2	no	—
520	M₁₆	—	30	2	no	—
521	C₂×C₈	—	3	1	no	—
522	C₂×C₈	—	3	4	no	—
523	C₂×C₈	—	3	1	no	—
524	C₂×C₈	—	5	1	no	—
525	C₂×C₈	—	5	1	no	—
526	C₂×C₈	—	15	1	no	—
527	C₂×C₈	—	15	1	no	—
528	C₂×C₈	—	30	2	no	—
529	C₂×C₈	C₂×D₃×D₅	1	1	yes	characteristic
530	C₂×C₈	C₂×D₃×D₅	1	1	yes	characteristic
531	C₄⋊C₄	—	3	1	no	—
532	C₄⋊C₄	—	3	1	no	—
533	C₄⋊C₄	—	5	1	no	—
534	C₄⋊C₄	—	5	1	no	—
535	C₄⋊C₄	—	5	1	no	—
536	C₄⋊C₄	—	15	1	no	—
537	C₄⋊C₄	—	15	1	no	—
538	C₄⋊C₄	—	15	1	no	—
539	C₄⋊C₄	—	15	1	no	—
540	C₄⋊C₄	—	15	1	no	—
541	C₄⋊C₄	—	15	1	no	—
542	C₄⋊C₄	—	15	1	no	—
543	C₄⋊C₄	—	15	1	no	—
544	C₄⋊C₄	—	15	1	no	—
545	C₄⋊C₄	—	15	1	no	—
546	C₄⋊C₄	—	15	1	no	—
547	C₂²⋊C₄	—	3	1	no	—
548	C₂²⋊C₄	—	3	1	no	—
549	C₂²⋊C₄	—	15	1	no	—
550	C₂²⋊C₄	—	15	1	no	—
551	C₄²	—	3	1	no	—
552	C₄²	—	5	1	no	—
553	C₄²	—	5	1	no	—
554	C₄²	—	15	1	no	—
555	C₄²	—	15	1	no	—
556	C₄²	—	15	1	no	—
557	C₄²	—	15	1	no	—
558	C₄²	C₂×D₃×D₅	1	1	yes	characteristic
559	C₃×C₅	#2960	1	1	yes	characteristic, complemented, Hall
560	C₂²×C₃	C₂²×C₄×D₅	1	1	yes	characteristic
561	C₂×D₃	—	2	1	no	—
562	C₂×D₃	—	2	1	no	—
563	C₂×D₃	C₄×Dic₁₀	1	2	yes	—
564	C₃×C₄	—	2	1	no	—
565	C₃×C₄	—	2	1	no	—
566	C₃×C₄	—	5	2	no	—
567	C₃×C₄	—	10	1	no	—
568	C₃×C₄	—	10	1	no	—
569	C₃×C₄	—	10	1	no	—
570	C₃×C₄	C₂²×Dic₁₀	1	1	yes	characteristic
571	C₃×C₄	C₂×#709	1	1	yes	characteristic
572	Dic₃	—	2	1	no	—
573	Dic₃	—	2	1	no	—
574	Dic₃	—	5	2	no	—
575	Dic₃	—	10	1	no	—
576	Dic₃	—	10	1	no	—
577	Dic₃	—	10	1	no	—
578	Dic₃	C₄×Dic₁₀	1	2	yes	—
579	C₂×C₅	—	6	2	no	—
580	C₂×C₅	C₄×D₃×Q₈	1	1	yes	characteristic
581	C₂×C₅	C₂×#901	1	1	yes	characteristic
582	C₂×C₅	D₃×#131	1	1	yes	characteristic
583	C₂³	—	3	1	no	—
584	Q₈	—	10	2	no	—
585	Q₈	—	30	2	no	—
586	Q₈	—	30	2	no	—
587	Q₈	—	30	2	no	—
588	C₂×C₄	—	3	1	no	—
589	C₂×C₄	—	3	2	no	—
590	C₂×C₄	—	3	2	no	—
591	C₂×C₄	—	3	1	no	—
592	C₂×C₄	—	3	1	no	—
593	C₂×C₄	—	5	1	no	—
594	C₂×C₄	—	5	1	no	—
595	C₂×C₄	—	5	1	no	—
596	C₂×C₄	—	5	1	no	—
597	C₂×C₄	—	15	1	no	—
598	C₂×C₄	—	15	1	no	—
599	C₂×C₄	—	15	1	no	—
600	C₂×C₄	—	15	1	no	—
601	C₂×C₄	—	30	2	no	—
602	C₂×C₄	—	30	2	no	—
603	C₂×C₄	C₄×D₃×D₅	1	1	yes	characteristic
604	C₂×C₄	C₄×D₃×D₅	1	1	yes	characteristic
605	C₂×C₄	C₂²×D₃×D₅	1	1	yes	characteristic
606	C₈	—	2	1	no	—
607	C₈	—	3	2	no	—
608	C₈	—	6	1	no	—
609	C₈	—	10	1	no	—
610	C₈	—	10	1	no	—
611	C₈	—	30	1	no	—
612	C₈	—	30	1	no	—
613	C₈	D₃×Dic₁₀	1	2	yes	—
614	C₂×C₃	C₂×C₄×Dic₁₀	1	1	yes	characteristic
615	C₂×C₃	D₅×#131	1	1	yes	characteristic
616	C₂×C₃	D₅×#131	1	1	yes	characteristic
617	D₃	—	2	2	no	—
618	C₅	#79917	1	1	yes	characteristic, complemented, Sylow
619	C₂²	—	3	2	no	—
620	C₂²	—	6	1	no	—
621	C₂²	—	6	1	no	—
622	C₂²	C₂×C₄×D₃×D₅	1	1	yes	characteristic
623	C₄	—	2	1	no	—
624	C₄	—	2	1	no	—
625	C₄	—	3	2	no	—
626	C₄	—	5	2	no	—
627	C₄	—	6	1	no	—
628	C₄	—	6	1	no	—
629	C₄	—	10	1	no	—
630	C₄	—	10	1	no	—
631	C₄	—	10	1	no	—
632	C₄	—	15	2	no	—
633	C₄	—	30	1	no	—
634	C₄	—	30	1	no	—
635	C₄	—	30	1	no	—
636	C₄	C₂×D₃×Dic₁₀	1	1	yes	characteristic
637	C₄	D₃×#709	1	1	yes	characteristic
638	C₃	#10610273	1	1	yes	characteristic, complemented, Sylow
639	C₂	—	6	2	no	—
640	C₂	C₄×D₃×Dic₁₀	1	1	yes	characteristic
641	C₂	D₅×#901	1	1	yes	characteristic
642	C₂	#11753952	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₈	C₂×D₃×D₅
commutator, socle	C₂²×C₃×C₅	C₂³×C₄
Frattini	C₂×C₄	C₂²×D₃×D₅
Fitting	C₃×C₄×C₅×C₈	C₂²
prime radical	C₂²×C₅×D₃	C₂²×C₄
cosocle	C₂×C₃×C₄×C₅	C₂⁴
hypercenter	C₄×C₈	D₃×D₅
hypocenter	C₃×C₅	#2960
LCS	G ▷ C₂²×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂×C₈ ◁ C₄×C₈

Complements

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

N	H ≅ G/N	type
2. C₈×Dic₃₀	C₂	semidirect
4. C₃×C₈×Dic₁₀	C₂	semidirect
5. #11747827	C₂	semidirect
6. C₈×#1204	C₂	semidirect
7. C₈×#1204	C₂	semidirect
12. #11747567	C₂	semidirect
14. #11746856	C₂	semidirect
15. #11746847	C₂	semidirect
75. C₈×Dic₁₀	D₃	semidirect
101. C₅×D₃×C₈	Q₈	semidirect
383. D₃×C₈	Dic₁₀	semidirect
559. C₃×C₅	#2960	semidirect
618. C₅	#79917	semidirect
638. C₃	#10610273	semidirect

Maximal subgroups

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

subgroup	index
#11752578	2
C₈×Dic₃₀	2
C₅×#4689	2
C₃×C₈×Dic₁₀	2
#11747827	2
C₈×#1204	2
#11747661	2
#11747653	2
#11747590	2
D₃×C₈×Dic₅	2
#11747567	2
#11746993	2
#11746856	2
#11746847	2
#10610273	3
#79917	5