Subgroups — C₈×#6769 #14418919

Order 1920.

912 conjugacy classes of subgroups.

The subgroup lattice has 504 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×#6769	C₂	1	1	yes	maximal, characteristic
2	C₈×D₆₀	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×C₅×D₃×C₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₈×Dic₁₀	C₂	1	1	yes	maximal, characteristic, complemented
5	#11747700	C₂	1	2	yes	maximal, complemented
6	C₈×#1203	C₂	1	2	yes	maximal, complemented
7	#11747584	C₂	1	2	yes	maximal, complemented
8	C₈×#1200	C₂	1	2	yes	maximal, complemented
9	#11746994	C₂	1	1	yes	maximal, characteristic, complemented
10	#11746853	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃⋊C₈×Dic₁₀	C₂	1	1	yes	maximal, characteristic, complemented
12	C₈×#709	—	3	1	no	maximal, Hall
13	C₂×#6769	C₄	1	1	yes	characteristic
14	C₂×C₈×D₁₅	C₂²	1	2	yes	—
15	C₄×D₆₀	C₂²	1	1	yes	characteristic
16	C₂×C₅×D₃×C₈	C₂²	1	1	yes	characteristic
17	C₂×C₅×D₃×C₈	C₂²	1	1	yes	characteristic
18	C₄²×C₅×D₃	C₂²	1	1	yes	characteristic
19	C₃×C₄×Dic₁₀	C₂²	1	1	yes	characteristic
20	#91446	C₄	1	2	yes	—
21	C₄×#1203	C₂²	1	2	yes	—
22	#91428	C₄	1	1	yes	characteristic
23	#91403	C₄	1	2	yes	—
24	C₄×#1200	C₂²	1	2	yes	—
25	#91338	C₄	1	1	yes	characteristic
26	Dic₃×Dic₁₀	C₄	1	1	yes	characteristic
27	C₂×#6648	C₂²	1	2	yes	—
28	C₃×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
29	#91104	C₂²	1	2	yes	—
30	C₄⋊(C₃⋊#168)	C₂²	1	1	yes	characteristic
31	C₅×C₈×Dic₃	C₂²	1	1	yes	characteristic
32	C₅×C₈×Dic₃	C₂²	1	1	yes	characteristic
33	C₄×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic
34	C₃×#3946	C₂²	1	2	yes	—
35	C₃×C₈×Dic₅	C₂²	1	2	yes	—
36	C₃×C₄⋊#168	C₂²	1	1	yes	characteristic
37	#90982	C₂²	1	2	yes	—
38	#90957	C₂²	1	2	yes	—
39	(C₂×D₃)⋊#168	C₂²	1	2	yes	—
40	Dic₃×#168	C₂²	1	2	yes	—
41	Dic₅×C₃⋊C₈	C₂²	1	2	yes	—
42	C₈×#239	—	5	1	no	maximal, Hall
43	C₄×#709	—	3	1	no	—
44	C₂×C₄×C₅×C₈	—	3	1	no	—
45	C₈×C₂²⋊D₅	—	3	2	no	—
46	C₈×C₂²⋊D₅	—	3	2	no	—
47	#65214	—	3	1	no	—
48	C₈×D₂₀	—	3	1	no	—
49	C₈×D₂₀	—	3	1	no	—
50	#64974	—	3	2	no	—
51	C₄×C₈×D₅	—	3	2	no	—
52	C₈×Dic₁₀	—	3	1	no	—
53	C₈×Dic₁₀	D₃	1	1	yes	characteristic, complemented
54	C₂×D₆₀	C₂×C₄	1	1	yes	characteristic
55	C₂×C₄×D₁₅	C₂³	1	2	yes	—
56	C₂×C₄×C₅×D₃	C₂×C₄	1	1	yes	characteristic
57	C₂×C₄×C₅×D₃	C₂×C₄	1	1	yes	characteristic
58	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
59	C₂×C₃×Dic₁₀	C₂×C₄	1	1	yes	characteristic
60	C₂×#1203	C₂×C₄	1	2	yes	—
61	C₂×#1200	C₂×C₄	1	2	yes	—
62	C₂×#1200	C₂×C₄	1	2	yes	—
63	#6769	C₈	1	8	yes	direct product factor
64	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
65	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
66	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
67	#6714	C₂×C₄	1	2	yes	—
68	C₄⋊Dic₁₅	C₂×C₄	1	1	yes	characteristic
69	C₂×C₃⋊#168	C₂³	1	2	yes	—
70	C₈×D₁₅	—	2	4	no	—
71	C₄×C₅×Dic₃	C₂×C₄	1	1	yes	characteristic
72	C₄×C₅×Dic₃	C₂×C₄	1	1	yes	characteristic
73	C₄×C₅×Dic₃	C₂³	1	1	yes	characteristic
74	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
75	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
76	C₅×D₃×C₈	—	2	2	no	—
77	C₅×D₃×C₈	—	2	2	no	—
78	C₃×C₄⋊Dic₅	C₂×C₄	1	1	yes	characteristic
79	C₃×#683	C₂×C₄	1	2	yes	—
80	C₃×C₄×Dic₅	C₂³	1	2	yes	—
81	C₂×C₃×#168	C₂³	1	2	yes	—
82	#6668	C₂×C₄	1	2	yes	—
83	#6667	C₂×C₄	1	2	yes	—
84	(C₂×D₃)⋊Dic₅	C₂×C₄	1	2	yes	—
85	Dic₃×Dic₅	C₂×C₄	1	2	yes	—
86	Dic₃×Dic₅	C₂×C₄	1	2	yes	—
87	#6648	—	2	4	no	—
88	C₄×#239	—	5	1	no	—
89	C₃×C₈×Q₈	—	5	1	no	—
90	Q₈×C₃⋊C₈	—	5	1	no	—
91	#4834	—	5	2	no	—
92	#4834	—	5	1	no	—
93	#4833	—	5	1	no	—
94	#4833	—	5	2	no	—
95	C₈×D₁₂	—	5	2	no	—
96	C₈×D₁₂	—	5	1	no	—
97	C₄×D₃×C₈	—	5	2	no	—
98	C₄×D₃×C₈	D₅	1	1	yes	characteristic, complemented
99	C₂×#709	—	3	1	no	—
100	C₂²×C₅×C₈	—	3	1	no	—
101	C₂²×C₅×C₈	—	3	1	no	—
102	C₂×C₄²×C₅	—	3	1	no	—
103	C₄×C₂²⋊D₅	—	3	2	no	—
104	C₄×C₂²⋊D₅	—	3	2	no	—
105	#4072	—	3	1	no	—
106	C₂×C₈×D₅	—	3	2	no	—
107	C₂×C₈×D₅	—	3	2	no	—
108	C₄×D₂₀	—	3	1	no	—
109	C₄×D₂₀	—	3	1	no	—
110	#4018	—	3	2	no	—
111	C₄²×D₅	—	3	2	no	—
112	C₄×Dic₁₀	—	3	1	no	—
113	C₄×Dic₁₀	C₂×D₃	1	1	yes	characteristic
114	C₄×C₅×C₈	—	3	1	no	—
115	C₄×C₅×C₈	—	3	1	no	—
116	C₄×C₅×C₈	—	3	1	no	—
117	C₄×C₅×C₈	C₂×D₃	1	1	yes	characteristic
118	C₂²⋊#168	—	3	2	no	—
119	#3952	—	3	2	no	—
120	#3952	—	3	2	no	—
121	#3946	—	3	2	no	—
122	#3946	C₂×D₃	1	2	yes	—
123	C₈×Dic₅	—	3	2	no	—
124	C₈×Dic₅	C₂×D₃	1	2	yes	—
125	C₄⋊#168	—	3	1	no	—
126	C₄⋊#168	C₂×D₃	1	1	yes	characteristic
127	C₄×#168	—	3	2	no	—
128	C₈×#41	—	15	1	no	Sylow
129	C₂²×D₁₅	C₂²×C₄	1	2	yes	—
130	C₂²×C₅×D₃	C₂²×C₄	1	1	yes	characteristic
131	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
132	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
133	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
134	C₂×Dic₁₅	C₂²×C₄	1	2	yes	—
135	D₆₀	C₂×C₈	1	4	yes	complemented
136	C₄×D₁₅	—	2	2	no	—
137	C₄×D₁₅	—	2	2	no	—
138	C₂×C₅×Dic₃	C₂²×C₄	1	1	yes	characteristic
139	C₂×C₅×Dic₃	C₂²×C₄	1	1	yes	characteristic
140	C₂×C₅×Dic₃	C₂²×C₄	1	1	yes	characteristic
141	C₄×C₅×D₃	—	2	1	no	—
142	C₄×C₅×D₃	—	2	1	no	—
143	C₄×C₅×D₃	—	2	2	no	—
144	C₄×C₅×D₃	C₂×C₈	1	4	yes	complemented
145	C₂×C₃×Dic₅	C₂²×C₄	1	2	yes	—
146	C₂×C₃×Dic₅	C₂²×C₄	1	2	yes	—
147	C₃×Dic₁₀	C₂×C₈	1	4	yes	complemented
148	#1203	C₂×C₈	1	8	yes	complemented
149	#1200	—	2	4	no	—
150	#1200	C₂×C₈	1	8	yes	complemented
151	C₃×C₅×C₈	—	2	1	no	—
152	C₃×C₅×C₈	#41	1	2	yes	complemented
153	C₃⋊#168	—	2	2	no	—
154	C₃×#168	—	2	2	no	—
155	C₅×C₃⋊C₈	—	2	1	no	—
156	C₅×C₃⋊C₈	#41	1	2	yes	complemented
157	C₂×#239	—	5	1	no	—
158	C₃×C₄×Q₈	—	5	1	no	—
159	Q₈×Dic₃	—	5	1	no	—
160	C₂×D₃×C₈	—	5	2	no	—
161	C₂×D₃×C₈	—	5	2	no	—
162	C₂×D₃×C₈	C₂×D₅	1	1	yes	characteristic
163	C₂×D₃×C₈	C₂×D₅	1	1	yes	characteristic
164	#893	—	5	2	no	—
165	#893	—	5	1	no	—
166	#892	—	5	1	no	—
167	#892	—	5	2	no	—
168	C₄×D₁₂	—	5	2	no	—
169	C₄×D₁₂	—	5	1	no	—
170	C₄²×D₃	—	5	2	no	—
171	C₄²×D₃	C₂×D₅	1	1	yes	characteristic
172	C₃×C₄⋊C₈	—	5	2	no	—
173	C₃×C₄⋊C₈	—	5	1	no	—
174	C₃×C₄×C₈	—	5	2	no	—
175	C₃×C₄×C₈	C₂×D₅	1	1	yes	characteristic
176	(C₂×D₃)⋊C₈	—	5	2	no	—
177	(C₂×D₃)⋊C₈	—	5	2	no	—
178	(C₂×D₃)⋊C₈	—	5	2	no	—
179	C₈×Dic₃	—	5	2	no	—
180	C₈×Dic₃	C₂×D₅	1	1	yes	characteristic
181	C₈×Dic₃	C₂×D₅	1	1	yes	characteristic
182	C₄⋊(C₃⋊C₈)	—	5	1	no	—
183	C₄⋊(C₃⋊C₈)	—	5	2	no	—
184	C₄×C₃⋊C₈	—	5	2	no	—
185	C₄×C₃⋊C₈	C₂×D₅	1	1	yes	characteristic
186	C₂²×C₄×C₅	—	3	1	no	—
187	C₂²×C₄×C₅	—	3	1	no	—
188	C₂²×C₄×C₅	—	3	1	no	—
189	C₂×C₂²⋊D₅	—	3	2	no	—
190	#709	—	3	8	no	—
191	C₂×D₂₀	—	3	1	no	—
192	C₂×C₄×D₅	—	3	2	no	—
193	C₂×C₄×D₅	—	3	2	no	—
194	C₂×C₄×D₅	—	3	2	no	—
195	C₂×Dic₁₀	C₄×D₃	1	1	yes	characteristic
196	C₂×C₅×C₈	—	3	1	no	—
197	C₂×C₅×C₈	—	3	1	no	—
198	C₂×C₅×C₈	—	6	2	no	—
199	C₂×C₅×C₈	—	6	2	no	—
200	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
201	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
202	C₄²×C₅	—	3	1	no	—
203	C₄²×C₅	—	3	1	no	—
204	C₄²×C₅	—	3	1	no	—
205	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
206	C₂²⋊Dic₅	—	3	2	no	—
207	#685	—	3	2	no	—
208	#685	—	3	2	no	—
209	C₄⋊Dic₅	—	3	1	no	—
210	C₄⋊Dic₅	C₄×D₃	1	1	yes	characteristic
211	#683	—	3	2	no	—
212	#683	C₄×D₃	1	2	yes	—
213	C₄×Dic₅	—	3	2	no	—
214	C₄×Dic₅	—	3	2	no	—
215	C₄×Dic₅	C₂²×D₃	1	2	yes	—
216	C₂×#168	—	3	2	no	—
217	C₂×#168	C₂²×D₃	1	2	yes	—
218	C₈×D₅	—	6	4	no	—
219	C₈×D₅	—	6	4	no	—
220	C₄×#41	—	15	1	no	—
221	C₈×Q₈	—	5	1	no	—
222	C₈×Q₈	—	15	1	no	—
223	C₈×D₄	—	15	1	no	—
224	C₈×D₄	—	15	2	no	—
225	C₈×D₄	—	15	2	no	—
226	C₈×D₄	—	15	1	no	—
227	#431	—	15	2	no	—
228	#431	—	15	1	no	—
229	C₂×C₄×C₈	—	3	1	no	—
230	C₂×C₄×C₈	—	15	2	no	—
231	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
232	C₂×D₁₅	—	2	2	no	—
233	C₂×D₁₅	—	2	2	no	—
234	C₂×D₁₅	C₂²×C₈	1	4	yes	—
235	C₂×C₅×D₃	—	2	1	no	—
236	C₂×C₅×D₃	—	2	1	no	—
237	C₂×C₅×D₃	C₂²×C₈	1	2	yes	—
238	C₃×C₄×C₅	—	2	1	no	—
239	C₃×C₄×C₅	C₂²×C₈	1	2	yes	—
240	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
241	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
242	Dic₁₅	—	2	2	no	—
243	C₃×Dic₅	—	2	2	no	—
244	C₃×Dic₅	C₂²×C₈	1	4	yes	—
245	C₅×Dic₃	—	2	1	no	—
246	C₅×Dic₃	C₂²×C₈	1	2	yes	—
247	C₅×Dic₃	#131	1	2	yes	—
248	C₂×C₃×Q₈	—	5	1	no	—
249	#239	—	5	8	no	—
250	C₂×D₁₂	—	5	2	no	—
251	C₂×D₁₂	—	5	1	no	—
252	C₂×C₄×D₃	—	5	2	no	—
253	C₂×C₄×D₃	—	5	2	no	—
254	C₂×C₄×D₃	—	5	2	no	—
255	C₂×C₄×D₃	C₄×D₅	1	1	yes	characteristic
256	C₂×C₄×D₃	C₄×D₅	1	1	yes	characteristic
257	C₂×C₄×D₃	C₂²×D₅	1	1	yes	characteristic
258	C₂×C₃×C₈	—	5	2	no	—
259	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
260	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
261	C₃×C₄⋊C₄	—	5	2	no	—
262	C₃×C₄⋊C₄	—	5	1	no	—
263	C₃×C₄²	—	5	2	no	—
264	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
265	(C₂×D₃)⋊C₄	—	5	2	no	—
266	(C₂×D₃)⋊C₄	—	5	2	no	—
267	(C₂×D₃)⋊C₄	—	5	2	no	—
268	C₄⋊Dic₃	—	5	1	no	—
269	C₄⋊Dic₃	—	5	2	no	—
270	C₄×Dic₃	—	5	2	no	—
271	C₄×Dic₃	—	5	2	no	—
272	C₄×Dic₃	C₄×D₅	1	1	yes	characteristic
273	C₄×Dic₃	C₄×D₅	1	1	yes	characteristic
274	C₄×Dic₃	C₂²×D₅	1	1	yes	characteristic
275	C₂×C₃⋊C₈	—	5	2	no	—
276	C₂×C₃⋊C₈	C₂²×D₅	1	1	yes	characteristic
277	C₂×C₃⋊C₈	C₂²×D₅	1	1	yes	characteristic
278	D₃×C₈	—	2	2	no	—
279	D₃×C₈	—	2	2	no	—
280	D₃×C₈	—	10	4	no	—
281	D₃×C₈	—	10	4	no	—
282	C₂³×C₅	—	3	1	no	—
283	C₂²×D₅	—	3	2	no	—
284	C₂×C₄×C₅	—	3	1	no	—
285	C₂×C₄×C₅	—	3	1	no	—
286	C₂×C₄×C₅	—	3	4	no	—
287	C₂×C₄×C₅	—	3	1	no	—
288	C₂×C₄×C₅	—	6	2	no	—
289	C₂×C₄×C₅	—	6	1	no	—
290	C₂×C₄×C₅	—	6	1	no	—
291	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
292	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
293	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
294	C₂²⋊D₅	—	3	8	no	—
295	C₂×Dic₅	—	3	2	no	—
296	C₂×Dic₅	C₂×C₄×D₃	1	2	yes	—
297	C₂×Dic₅	C₂×C₄×D₃	1	2	yes	—
298	D₂₀	—	3	4	no	—
299	C₄×D₅	—	3	8	no	—
300	C₄×D₅	—	6	4	no	—
301	C₄×D₅	—	6	2	no	—
302	C₄×D₅	—	6	2	no	—
303	Dic₁₀	D₃×C₈	1	4	yes	complemented
304	C₅×C₈	—	2	1	no	—
305	C₅×C₈	—	3	2	no	—
306	C₅×C₈	—	6	1	no	—
307	C₅×C₈	#239	1	2	yes	complemented
308	#168	—	2	2	no	—
309	#168	—	6	2	no	—
310	C₂×#41	—	15	1	no	—
311	C₂²×C₈	—	3	1	no	—
312	C₂²×C₈	—	3	1	no	—
313	C₂²×C₈	—	15	2	no	—
314	C₂²×C₈	—	15	2	no	—
315	C₄×Q₈	—	5	1	no	—
316	C₄×Q₈	—	15	1	no	—
317	C₄×D₄	—	15	1	no	—
318	C₄×D₄	—	15	2	no	—
319	C₄×D₄	—	15	2	no	—
320	C₄×D₄	—	15	1	no	—
321	#117	—	15	2	no	—
322	#117	—	15	1	no	—
323	C₂×C₄²	—	3	1	no	—
324	C₂×C₄²	—	15	2	no	—
325	C₄⋊C₈	—	5	2	no	—
326	C₄⋊C₈	—	5	1	no	—
327	C₄⋊C₈	—	15	2	no	—
328	C₄⋊C₈	—	15	1	no	—
329	C₂²⋊C₈	—	15	2	no	—
330	C₂²⋊C₈	—	15	2	no	—
331	C₂²⋊C₈	—	15	2	no	—
332	C₄×C₈	—	3	1	no	—
333	C₄×C₈	—	3	1	no	—
334	C₄×C₈	—	3	1	no	—
335	C₄×C₈	—	5	2	no	—
336	C₄×C₈	—	15	2	no	—
337	C₄×C₈	—	15	2	no	—
338	C₄×C₈	D₃×D₅	1	1	yes	characteristic
339	C₂×C₃×C₅	C₄×#41	1	1	yes	characteristic
340	C₂×C₃×C₅	C₂³×C₈	1	1	yes	characteristic
341	C₂×C₃×C₅	C₂×#131	1	1	yes	characteristic
342	D₁₅	—	2	4	no	—
343	C₅×D₃	—	2	2	no	—
344	C₂²×D₃	—	5	2	no	—
345	C₂²×D₃	C₂×C₄×D₅	1	1	yes	characteristic
346	C₃×Q₈	—	5	4	no	—
347	C₂×C₃×C₄	—	5	2	no	—
348	C₂×C₃×C₄	—	5	2	no	—
349	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
350	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
351	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
352	C₂×Dic₃	—	5	2	no	—
353	C₂×Dic₃	C₂×C₄×D₅	1	1	yes	characteristic
354	C₂×Dic₃	C₂×C₄×D₅	1	1	yes	characteristic
355	C₂×Dic₃	C₂×C₄×D₅	1	1	yes	characteristic
356	D₁₂	—	5	8	no	—
357	D₁₂	—	5	4	no	—
358	C₄×D₃	—	2	1	no	—
359	C₄×D₃	—	2	1	no	—
360	C₄×D₃	—	2	2	no	—
361	C₄×D₃	—	5	8	no	—
362	C₄×D₃	—	10	2	no	—
363	C₄×D₃	—	10	2	no	—
364	C₄×D₃	—	10	4	no	—
365	C₄×D₃	C₈×D₅	1	4	yes	complemented
366	C₃×C₈	—	2	1	no	—
367	C₃×C₈	—	10	2	no	—
368	C₃×C₈	#709	1	2	yes	complemented
369	C₃⋊C₈	—	2	1	no	—
370	C₃⋊C₈	—	10	2	no	—
371	C₃⋊C₈	#709	1	2	yes	complemented
372	C₂²×C₅	—	3	2	no	—
373	C₂²×C₅	—	6	1	no	—
374	C₂²×C₅	—	6	1	no	—
375	C₂²×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
376	C₂×D₅	—	3	4	no	—
377	C₂×D₅	—	6	2	no	—
378	C₂×D₅	—	6	2	no	—
379	C₄×C₅	—	2	1	no	—
380	C₄×C₅	—	3	2	no	—
381	C₄×C₅	—	3	2	no	—
382	C₄×C₅	—	6	1	no	—
383	C₄×C₅	C₂×D₃×C₈	1	2	yes	—
384	C₄×C₅	C₂×#239	1	1	yes	characteristic
385	C₄×C₅	D₃×#41	1	1	yes	characteristic
386	Dic₅	—	2	2	no	—
387	Dic₅	—	6	2	no	—
388	Dic₅	C₂×D₃×C₈	1	4	yes	—
389	#41	—	15	8	no	—
390	C₂×Q₈	—	5	1	no	—
391	C₂×D₄	—	15	2	no	—
392	C₂×D₄	—	15	1	no	—
393	C₂²×C₄	—	3	1	no	—
394	C₂²×C₄	—	3	1	no	—
395	C₂²×C₄	—	3	1	no	—
396	C₂²×C₄	—	15	2	no	—
397	C₂²×C₄	—	15	2	no	—
398	C₂²×C₄	—	15	2	no	—
399	C₂×C₈	—	3	1	no	—
400	C₂×C₈	—	3	1	no	—
401	C₂×C₈	—	5	2	no	—
402	C₂×C₈	—	6	2	no	—
403	C₂×C₈	—	6	2	no	—
404	C₂×C₈	—	15	2	no	—
405	C₂×C₈	—	30	4	no	—
406	C₂×C₈	—	30	4	no	—
407	C₂×C₈	C₂×D₃×D₅	1	1	yes	characteristic
408	C₂×C₈	C₂×D₃×D₅	1	1	yes	characteristic
409	C₄⋊C₄	—	5	2	no	—
410	C₄⋊C₄	—	5	1	no	—
411	C₄⋊C₄	—	15	2	no	—
412	C₄⋊C₄	—	15	1	no	—
413	C₂²⋊C₄	—	15	2	no	—
414	C₂²⋊C₄	—	15	2	no	—
415	C₂²⋊C₄	—	15	2	no	—
416	C₄²	—	3	1	no	—
417	C₄²	—	3	1	no	—
418	C₄²	—	3	1	no	—
419	C₄²	—	5	2	no	—
420	C₄²	—	15	2	no	—
421	C₄²	—	15	2	no	—
422	C₄²	C₂×D₃×D₅	1	1	yes	characteristic
423	C₃×C₅	C₈×#41	1	1	yes	characteristic, complemented, Hall
424	C₂²×C₃	C₂²×C₄×D₅	1	1	yes	characteristic
425	C₂×D₃	—	2	1	no	—
426	C₂×D₃	—	2	1	no	—
427	C₂×D₃	—	5	4	no	—
428	C₂×D₃	—	10	2	no	—
429	C₂×D₃	—	10	2	no	—
430	C₂×D₃	C₂×C₈×D₅	1	2	yes	—
431	C₃×C₄	—	2	1	no	—
432	C₃×C₄	—	5	4	no	—
433	C₃×C₄	—	10	2	no	—
434	C₃×C₄	C₂×C₈×D₅	1	2	yes	—
435	C₃×C₄	C₂×#709	1	1	yes	characteristic
436	C₃×C₄	C₂×#709	1	1	yes	characteristic
437	Dic₃	—	2	1	no	—
438	Dic₃	—	10	2	no	—
439	Dic₃	C₂×C₈×D₅	1	2	yes	—
440	Dic₃	#4047	1	2	yes	—
441	C₂×C₅	—	6	2	no	—
442	C₂×C₅	C₄×#239	1	1	yes	characteristic
443	C₂×C₅	C₂²×D₃×C₈	1	1	yes	characteristic
444	C₂×C₅	D₃×#131	1	1	yes	characteristic
445	D₅	—	6	4	no	—
446	C₂³	—	3	1	no	—
447	C₂³	—	15	2	no	—
448	Q₈	—	5	4	no	—
449	D₄	—	15	8	no	—
450	D₄	—	15	4	no	—
451	C₂×C₄	—	3	1	no	—
452	C₂×C₄	—	3	1	no	—
453	C₂×C₄	—	3	4	no	—
454	C₂×C₄	—	3	1	no	—
455	C₂×C₄	—	5	2	no	—
456	C₂×C₄	—	5	2	no	—
457	C₂×C₄	—	6	2	no	—
458	C₂×C₄	—	6	1	no	—
459	C₂×C₄	—	6	1	no	—
460	C₂×C₄	—	15	8	no	—
461	C₂×C₄	—	15	2	no	—
462	C₂×C₄	—	30	4	no	—
463	C₂×C₄	—	30	2	no	—
464	C₂×C₄	—	30	2	no	—
465	C₂×C₄	C₄×D₃×D₅	1	1	yes	characteristic
466	C₂×C₄	C₄×D₃×D₅	1	1	yes	characteristic
467	C₂×C₄	C₂²×D₃×D₅	1	1	yes	characteristic
468	C₈	—	2	1	no	—
469	C₈	—	3	2	no	—
470	C₈	—	6	1	no	—
471	C₈	—	10	2	no	—
472	C₈	—	30	2	no	—
473	C₈	#6769	1	2	yes	direct product factor
474	C₂×C₃	C₄×#709	1	1	yes	characteristic
475	C₂×C₃	C₂²×C₈×D₅	1	1	yes	characteristic
476	C₂×C₃	C₂×#4047	1	1	yes	characteristic
477	D₃	—	2	2	no	—
478	D₃	—	10	4	no	—
479	C₅	C₈×#239	1	1	yes	characteristic, complemented, Sylow
480	C₂²	—	3	2	no	—
481	C₂²	—	6	1	no	—
482	C₂²	—	6	1	no	—
483	C₂²	—	15	4	no	—
484	C₂²	—	30	2	no	—
485	C₂²	—	30	2	no	—
486	C₂²	C₂×C₄×D₃×D₅	1	1	yes	characteristic
487	C₄	—	2	1	no	—
488	C₄	—	3	2	no	—
489	C₄	—	3	2	no	—
490	C₄	—	5	4	no	—
491	C₄	—	6	1	no	—
492	C₄	—	10	2	no	—
493	C₄	—	30	2	no	—
494	C₄	D₃×C₈×D₅	1	2	yes	—
495	C₄	C₂×#6769	1	1	yes	characteristic
496	C₄	D₃×#709	1	1	yes	characteristic
497	C₃	C₈×#709	1	1	yes	characteristic, complemented, Sylow
498	C₂	—	6	2	no	—
499	C₂	—	30	4	no	—
500	C₂	C₄×#6769	1	1	yes	characteristic
501	C₂	C₂×D₃×C₈×D₅	1	1	yes	characteristic
502	C₂	D₃×#4047	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₈	C₂×D₃×D₅
commutator	C₂×C₃×C₅	C₂³×C₈
Frattini	C₂×C₄	C₂²×D₃×D₅
Fitting	C₃×C₄×C₅×C₈	C₂²
socle	C₂²×C₃×C₅	C₂³×C₄
prime radical	C₂×#6769	C₄
cosocle	C₂×C₃×C₄×C₅	C₂⁴
hypercenter	C₄×C₈	D₃×D₅
hypocenter	C₃×C₅	C₈×#41
LCS	G ▷ C₂×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×D₆₀	C₂	semidirect
3. C₄×C₅×D₃×C₈	C₂	semidirect
4. C₃×C₈×Dic₁₀	C₂	semidirect
5. #11747700	C₂	semidirect
6. C₈×#1203	C₂	semidirect
7. #11747584	C₂	semidirect
8. C₈×#1200	C₂	semidirect
9. #11746994	C₂	semidirect
10. #11746853	C₂	semidirect
11. C₃⋊C₈×Dic₁₀	C₂	semidirect
53. C₈×Dic₁₀	D₃	semidirect
63. #6769	C₈	direct (N × H)
98. C₄×D₃×C₈	D₅	semidirect
135. D₆₀	C₂×C₈	semidirect
144. C₄×C₅×D₃	C₂×C₈	semidirect
147. C₃×Dic₁₀	C₂×C₈	semidirect
148. #1203	C₂×C₈	semidirect
150. #1200	C₂×C₈	semidirect
152. C₃×C₅×C₈	#41	semidirect
156. C₅×C₃⋊C₈	#41	semidirect
303. Dic₁₀	D₃×C₈	semidirect
307. C₅×C₈	#239	semidirect
365. C₄×D₃	C₈×D₅	semidirect
368. C₃×C₈	#709	semidirect
371. C₃⋊C₈	#709	semidirect
423. C₃×C₅	C₈×#41	semidirect
473. C₈	#6769	direct (N × H)
479. C₅	C₈×#239	semidirect
497. C₃	C₈×#709	semidirect

Maximal subgroups

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

subgroup	index
C₄×#6769	2
C₈×D₆₀	2
C₄×C₅×D₃×C₈	2
C₃×C₈×Dic₁₀	2
#11747700	2
C₈×#1203	2
#11747584	2
C₈×#1200	2
#11746994	2
#11746853	2
C₃⋊C₈×Dic₁₀	2
C₈×#709	3
C₈×#239	5

Subgroups — C8×#6769 #14418919

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈×#6769 #14418919