Subgroups — C₈×#6819 #14418886

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×#6819	C₂	1	1	yes	maximal, characteristic
2	C₃×C₅×C₈×D₄	C₂	1	1	yes	maximal, characteristic, complemented
3	C₈×#1220	C₂	1	2	yes	maximal, complemented
4	C₂×C₈×Dic₁₅	C₂	1	2	yes	maximal, complemented
5	D₄×C₃⋊#168	C₂	1	1	yes	maximal, characteristic, complemented
6	#11750934	C₂	1	1	yes	maximal, characteristic, complemented
7	#11750931	C₂	1	1	yes	maximal, characteristic, complemented
8	#11750826	C₂	1	2	yes	maximal, complemented
9	#11750819	C₂	1	2	yes	maximal, complemented
10	C₄×C₈×D₁₅	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈×Dic₃₀	C₂	1	1	yes	maximal, characteristic, complemented
12	C₈×#711	—	3	1	no	maximal, Hall
13	C₂×#6819	C₄	1	1	yes	characteristic
14	C₂²×C₃×C₅×C₈	C₂²	1	2	yes	—
15	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
16	D₄×Dic₁₅	C₄	1	1	yes	characteristic
17	C₄×#1220	C₂²	1	2	yes	—
18	C₂×C₄×Dic₁₅	C₂²	1	2	yes	—
19	C₂²×C₃⋊#168	C₂²	1	2	yes	—
20	C₂×C₈×D₁₅	C₂²	1	1	yes	characteristic
21	C₂×C₈×D₁₅	C₂²	1	1	yes	characteristic
22	#91781	C₄	1	1	yes	characteristic
23	#91776	C₄	1	1	yes	characteristic
24	#91770	C₄	1	2	yes	—
25	#91766	C₄	1	2	yes	—
26	C₄²×D₁₅	C₂²	1	1	yes	characteristic
27	C₄×Dic₃₀	C₂²	1	1	yes	characteristic
28	C₃×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
29	C₃×C₅×C₂²⋊C₈	C₂²	1	2	yes	—
30	C₃×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
31	#91114	C₂²	1	2	yes	—
32	#91104	C₂²	1	2	yes	—
33	#91098	C₂²	1	2	yes	—
34	#91098	C₂²	1	2	yes	—
35	C₈×Dic₁₅	C₂²	1	2	yes	—
36	C₈×Dic₁₅	C₂²	1	2	yes	—
37	C₈×Dic₁₅	C₂²	1	1	yes	characteristic
38	C₈×Dic₁₅	C₂²	1	2	yes	—
39	C₈×Dic₁₅	C₂²	1	1	yes	characteristic
40	C₄⋊(C₃⋊#168)	C₂²	1	1	yes	characteristic
41	C₄×C₃⋊#168	C₂²	1	1	yes	characteristic
42	C₈×#237	—	5	1	no	maximal, Hall
43	C₄×#711	—	3	1	no	—
44	C₅×C₈×D₄	D₃	1	1	yes	characteristic, complemented
45	C₈×C₂²⋊D₅	—	3	2	no	—
46	C₂×C₈×Dic₅	—	3	2	no	—
47	D₄×#168	—	3	1	no	—
48	#65122	—	3	1	no	—
49	#65119	—	3	1	no	—
50	#65014	—	3	2	no	—
51	#65007	—	3	2	no	—
52	C₄×C₈×D₅	—	3	1	no	—
53	C₈×Dic₁₀	—	3	1	no	—
54	C₂×C₃×C₅×D₄	C₂×C₄	1	1	yes	characteristic
55	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
56	C₂×#1220	C₂×C₄	1	2	yes	—
57	C₂²×Dic₁₅	C₂×C₄	1	2	yes	—
58	C₂²×Dic₁₅	C₂×C₄	1	2	yes	—
59	#6819	C₈	1	8	yes	direct product factor
60	C₂×C₄×D₁₅	C₂×C₄	1	1	yes	characteristic
61	C₂×C₄×D₁₅	C₂×C₄	1	1	yes	characteristic
62	C₂×C₄×D₁₅	C₂³	1	1	yes	characteristic
63	C₂×Dic₃₀	C₂×C₄	1	1	yes	characteristic
64	C₂×C₃×C₅×C₈	—	2	4	no	—
65	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
66	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
67	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
68	C₃×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
69	C₃×C₅×C₂²⋊C₄	C₂×C₄	1	2	yes	—
70	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
71	#6719	C₂×C₄	1	2	yes	—
72	#6714	C₂×C₄	1	2	yes	—
73	C₄⋊Dic₁₅	C₂×C₄	1	1	yes	characteristic
74	#6712	C₂×C₄	1	2	yes	—
75	#6712	C₂×C₄	1	2	yes	—
76	C₄×Dic₁₅	C₂×C₄	1	1	yes	characteristic
77	C₄×Dic₁₅	C₂×C₄	1	1	yes	characteristic
78	C₄×Dic₁₅	C₂×C₄	1	2	yes	—
79	C₄×Dic₁₅	C₂×C₄	1	2	yes	—
80	C₄×Dic₁₅	C₂³	1	2	yes	—
81	C₄×Dic₁₅	C₂³	1	1	yes	characteristic
82	C₂×C₃⋊#168	—	2	4	no	—
83	C₂×C₃⋊#168	C₂³	1	1	yes	characteristic
84	C₂×C₃⋊#168	C₂³	1	2	yes	—
85	C₂×C₃⋊#168	C₂³	1	1	yes	characteristic
86	C₈×D₁₅	—	2	2	no	—
87	C₈×D₁₅	—	2	2	no	—
88	C₄×#237	—	5	1	no	—
89	C₃×C₈×D₄	D₅	1	1	yes	characteristic, complemented
90	C₈×#67	—	5	2	no	—
91	C₂×C₈×Dic₃	—	5	2	no	—
92	D₄×C₃⋊C₈	—	5	1	no	—
93	#4833	—	5	1	no	—
94	#4830	—	5	1	no	—
95	#67⋊C₈	—	5	2	no	—
96	#4718	—	5	2	no	—
97	C₄×D₃×C₈	—	5	1	no	—
98	C₈×Dic₆	—	5	1	no	—
99	C₂×#711	—	3	1	no	—
100	C₂²×C₅×C₈	C₂×D₃	1	2	yes	—
101	C₄×C₅×D₄	C₂×D₃	1	1	yes	characteristic
102	D₄×Dic₅	—	3	1	no	—
103	C₄×C₂²⋊D₅	—	3	2	no	—
104	C₂×C₄×Dic₅	—	3	2	no	—
105	C₂²×#168	—	3	2	no	—
106	C₂×C₈×D₅	—	3	1	no	—
107	C₂×C₈×D₅	—	3	1	no	—
108	#4038	—	3	1	no	—
109	#4033	—	3	1	no	—
110	#4027	—	3	2	no	—
111	#4023	—	3	2	no	—
112	C₄²×D₅	—	3	1	no	—
113	C₄×Dic₁₀	—	3	1	no	—
114	C₅×C₄⋊C₈	C₂×D₃	1	1	yes	characteristic
115	C₅×C₂²⋊C₈	C₂×D₃	1	2	yes	—
116	C₄×C₅×C₈	C₂×D₃	1	1	yes	characteristic
117	C₂²⋊#168	—	3	2	no	—
118	#3952	—	3	2	no	—
119	#3946	—	3	2	no	—
120	#3946	—	3	2	no	—
121	C₈×Dic₅	—	3	2	no	—
122	C₈×Dic₅	—	3	2	no	—
123	C₈×Dic₅	—	3	1	no	—
124	C₈×Dic₅	—	3	2	no	—
125	C₈×Dic₅	—	3	1	no	—
126	C₄⋊#168	—	3	1	no	—
127	C₄×#168	—	3	1	no	—
128	C₈×#41	—	15	1	no	Sylow
129	C₂³×C₃×C₅	C₂²×C₄	1	2	yes	—
130	C₂²×D₁₅	C₂²×C₄	1	1	yes	characteristic
131	C₃×C₅×D₄	C₂×C₈	1	4	yes	complemented
132	C₂×C₃×C₄×C₅	—	2	2	no	—
133	C₂×C₃×C₄×C₅	—	2	2	no	—
134	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
135	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
136	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
137	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
138	#1220	C₂×C₈	1	8	yes	complemented
139	C₂×Dic₁₅	—	2	4	no	—
140	C₂×Dic₁₅	C₂×C₈	1	8	yes	complemented
141	C₂×Dic₁₅	C₂²×C₄	1	1	yes	characteristic
142	C₂×Dic₁₅	C₂²×C₄	1	2	yes	—
143	C₂×Dic₁₅	C₂²×C₄	1	1	yes	characteristic
144	C₂×Dic₁₅	C₂²×C₄	1	2	yes	—
145	C₂×Dic₁₅	C₂²×C₄	1	1	yes	characteristic
146	C₄×D₁₅	—	2	1	no	—
147	C₄×D₁₅	—	2	1	no	—
148	C₄×D₁₅	—	2	2	no	—
149	C₄×D₁₅	C₂×C₈	1	4	yes	complemented
150	Dic₃₀	C₂×C₈	1	4	yes	complemented
151	C₃×C₅×C₈	—	2	1	no	—
152	C₃×C₅×C₈	—	2	2	no	—
153	C₃×C₅×C₈	#41	1	2	yes	complemented
154	C₃⋊#168	—	2	1	no	—
155	C₃⋊#168	—	2	2	no	—
156	C₃⋊#168	#41	1	2	yes	complemented
157	C₂×#237	—	5	1	no	—
158	C₂²×C₃×C₈	C₂×D₅	1	2	yes	—
159	C₃×C₄×D₄	C₂×D₅	1	1	yes	characteristic
160	D₄×Dic₃	—	5	1	no	—
161	C₄×#67	—	5	2	no	—
162	C₂×C₄×Dic₃	—	5	2	no	—
163	C₂²×C₃⋊C₈	—	5	2	no	—
164	C₂×D₃×C₈	—	5	1	no	—
165	C₂×D₃×C₈	—	5	1	no	—
166	#892	—	5	1	no	—
167	#887	—	5	1	no	—
168	#67⋊C₄	—	5	2	no	—
169	#877	—	5	2	no	—
170	C₄²×D₃	—	5	1	no	—
171	C₄×Dic₆	—	5	1	no	—
172	C₃×C₄⋊C₈	C₂×D₅	1	1	yes	characteristic
173	C₃×C₂²⋊C₈	C₂×D₅	1	2	yes	—
174	C₃×C₄×C₈	C₂×D₅	1	1	yes	characteristic
175	#830	—	5	2	no	—
176	(C₂×D₃)⋊C₈	—	5	2	no	—
177	Dic₃⋊C₈	—	5	2	no	—
178	Dic₃⋊C₈	—	5	2	no	—
179	C₈×Dic₃	—	5	2	no	—
180	C₈×Dic₃	—	5	1	no	—
181	C₈×Dic₃	—	5	1	no	—
182	C₈×Dic₃	—	5	2	no	—
183	C₈×Dic₃	—	5	2	no	—
184	C₄⋊(C₃⋊C₈)	—	5	1	no	—
185	C₄×C₃⋊C₈	—	5	1	no	—
186	C₂×C₅×D₄	C₄×D₃	1	1	yes	characteristic
187	C₂²×C₄×C₅	C₂²×D₃	1	2	yes	—
188	C₂×C₂²⋊D₅	—	3	2	no	—
189	C₂²×Dic₅	—	3	2	no	—
190	C₂²×Dic₅	—	3	2	no	—
191	#711	—	3	8	no	—
192	C₂×C₄×D₅	—	3	1	no	—
193	C₂×C₄×D₅	—	3	1	no	—
194	C₂×C₄×D₅	—	3	1	no	—
195	C₂×Dic₁₀	—	3	1	no	—
196	C₂×C₅×C₈	—	2	4	no	—
197	C₂×C₅×C₈	C₂²×D₃	1	2	yes	—
198	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
199	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
200	C₅×C₄⋊C₄	C₄×D₃	1	1	yes	characteristic
201	C₅×C₂²⋊C₄	C₄×D₃	1	2	yes	—
202	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
203	C₂²⋊Dic₅	—	3	2	no	—
204	#685	—	3	2	no	—
205	C₄⋊Dic₅	—	3	1	no	—
206	#683	—	3	2	no	—
207	#683	—	3	2	no	—
208	C₄×Dic₅	—	3	1	no	—
209	C₄×Dic₅	—	3	1	no	—
210	C₄×Dic₅	—	3	2	no	—
211	C₄×Dic₅	—	3	2	no	—
212	C₄×Dic₅	—	3	1	no	—
213	C₄×Dic₅	—	3	2	no	—
214	C₂×#168	—	3	1	no	—
215	C₂×#168	—	3	1	no	—
216	C₂×#168	—	3	2	no	—
217	C₂×#168	—	6	4	no	—
218	C₈×D₅	—	6	2	no	—
219	C₈×D₅	—	6	2	no	—
220	C₄×#41	—	15	1	no	—
221	C₈×Q₈	—	15	1	no	—
222	C₈×Q₈	—	15	1	no	—
223	C₈×D₄	—	15	2	no	—
224	C₈×D₄	—	15	1	no	—
225	C₈×D₄	—	15	2	no	—
226	C₈×D₄	D₁₅	1	1	yes	characteristic, complemented
227	#431	—	15	1	no	—
228	#431	—	15	2	no	—
229	C₂×C₄×C₈	—	15	2	no	—
230	C₂×C₄×C₈	—	15	1	no	—
231	C₂²×C₃×C₅	—	2	2	no	—
232	C₂²×C₃×C₅	—	2	2	no	—
233	C₂²×C₃×C₅	C₂²×C₈	1	4	yes	—
234	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
235	C₂×D₁₅	—	2	1	no	—
236	C₂×D₁₅	—	2	1	no	—
237	C₂×D₁₅	C₂²×C₈	1	2	yes	—
238	C₃×C₄×C₅	—	2	2	no	—
239	C₃×C₄×C₅	—	2	1	no	—
240	C₃×C₄×C₅	C₂²×C₈	1	2	yes	—
241	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
242	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
243	Dic₁₅	—	2	1	no	—
244	Dic₁₅	—	2	2	no	—
245	Dic₁₅	C₂²×C₈	1	4	yes	—
246	Dic₁₅	C₂²×C₈	1	2	yes	—
247	Dic₁₅	#131	1	2	yes	—
248	C₂×C₃×D₄	C₄×D₅	1	1	yes	characteristic
249	C₂²×C₃×C₄	C₂²×D₅	1	2	yes	—
250	C₂×#67	—	5	2	no	—
251	C₂²×Dic₃	—	5	2	no	—
252	C₂²×Dic₃	—	5	2	no	—
253	#237	—	5	8	no	—
254	C₂×C₄×D₃	—	5	1	no	—
255	C₂×C₄×D₃	—	5	1	no	—
256	C₂×C₄×D₃	—	5	1	no	—
257	C₂×Dic₆	—	5	1	no	—
258	C₂×C₃×C₈	—	2	4	no	—
259	C₂×C₃×C₈	C₂²×D₅	1	2	yes	—
260	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
261	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
262	C₃×C₄⋊C₄	C₄×D₅	1	1	yes	characteristic
263	C₃×C₂²⋊C₄	C₄×D₅	1	2	yes	—
264	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
265	#217	—	5	2	no	—
266	(C₂×D₃)⋊C₄	—	5	2	no	—
267	C₄⋊Dic₃	—	5	1	no	—
268	Dic₃⋊C₄	—	5	2	no	—
269	Dic₃⋊C₄	—	5	2	no	—
270	C₄×Dic₃	—	5	1	no	—
271	C₄×Dic₃	—	5	1	no	—
272	C₄×Dic₃	—	5	2	no	—
273	C₄×Dic₃	—	5	2	no	—
274	C₄×Dic₃	—	5	1	no	—
275	C₄×Dic₃	—	5	2	no	—
276	C₂×C₃⋊C₈	—	5	1	no	—
277	C₂×C₃⋊C₈	—	5	1	no	—
278	C₂×C₃⋊C₈	—	5	2	no	—
279	C₂×C₃⋊C₈	—	10	4	no	—
280	D₃×C₈	—	10	2	no	—
281	D₃×C₈	—	10	2	no	—
282	C₂³×C₅	C₂×C₄×D₃	1	2	yes	—
283	C₂²×D₅	—	3	1	no	—
284	C₅×D₄	D₃×C₈	1	4	yes	complemented
285	C₂×C₄×C₅	—	2	2	no	—
286	C₂×C₄×C₅	—	2	2	no	—
287	C₂×C₄×C₅	C₂×C₄×D₃	1	2	yes	—
288	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
289	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
290	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
291	C₂²⋊D₅	—	3	8	no	—
292	C₂×Dic₅	—	3	8	no	—
293	C₂×Dic₅	—	3	1	no	—
294	C₂×Dic₅	—	3	1	no	—
295	C₂×Dic₅	—	3	2	no	—
296	C₂×Dic₅	—	3	1	no	—
297	C₂×Dic₅	—	3	2	no	—
298	C₂×Dic₅	—	6	4	no	—
299	C₄×D₅	—	3	4	no	—
300	C₄×D₅	—	6	2	no	—
301	C₄×D₅	—	6	1	no	—
302	C₄×D₅	—	6	1	no	—
303	Dic₁₀	—	3	4	no	—
304	C₅×C₈	—	2	2	no	—
305	C₅×C₈	—	2	1	no	—
306	C₅×C₈	#237	1	2	yes	complemented
307	#168	—	3	2	no	—
308	#168	—	6	1	no	—
309	#168	—	6	2	no	—
310	C₂×#41	—	15	1	no	—
311	C₂²×C₈	—	15	2	no	—
312	C₂²×C₈	—	15	1	no	—
313	C₂²×C₈	—	15	1	no	—
314	C₂²×C₈	C₂×D₁₅	1	2	yes	—
315	C₄×Q₈	—	15	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	C₂×D₁₅	1	1	yes	characteristic
321	#117	—	15	1	no	—
322	#117	—	15	2	no	—
323	C₂×C₄²	—	15	2	no	—
324	C₂×C₄²	—	15	1	no	—
325	C₄⋊C₈	—	15	2	no	—
326	C₄⋊C₈	—	15	2	no	—
327	C₄⋊C₈	—	15	1	no	—
328	C₄⋊C₈	C₂×D₁₅	1	1	yes	characteristic
329	C₂²⋊C₈	—	15	2	no	—
330	C₂²⋊C₈	—	15	2	no	—
331	C₂²⋊C₈	C₂×D₁₅	1	2	yes	—
332	C₄×C₈	—	15	2	no	—
333	C₄×C₈	—	15	1	no	—
334	C₄×C₈	—	15	2	no	—
335	C₄×C₈	—	15	1	no	—
336	C₄×C₈	—	15	2	no	—
337	C₄×C₈	—	15	1	no	—
338	C₄×C₈	C₂×D₁₅	1	1	yes	characteristic
339	C₂×C₃×C₅	—	2	4	no	—
340	C₂×C₃×C₅	C₄×#41	1	1	yes	characteristic
341	C₂×C₃×C₅	C₂³×C₈	1	1	yes	characteristic
342	C₂×C₃×C₅	C₂×#131	1	1	yes	characteristic
343	D₁₅	—	2	2	no	—
344	C₂³×C₃	C₂×C₄×D₅	1	2	yes	—
345	C₂²×D₃	—	5	1	no	—
346	C₃×D₄	C₈×D₅	1	4	yes	complemented
347	C₂×C₃×C₄	—	2	2	no	—
348	C₂×C₃×C₄	—	2	2	no	—
349	C₂×C₃×C₄	C₂×C₄×D₅	1	2	yes	—
350	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
351	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
352	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
353	#67	—	5	8	no	—
354	C₂×Dic₃	—	5	1	no	—
355	C₂×Dic₃	—	5	1	no	—
356	C₂×Dic₃	—	5	2	no	—
357	C₂×Dic₃	—	5	8	no	—
358	C₂×Dic₃	—	5	1	no	—
359	C₂×Dic₃	—	5	2	no	—
360	C₂×Dic₃	—	10	4	no	—
361	C₄×D₃	—	5	4	no	—
362	C₄×D₃	—	10	2	no	—
363	C₄×D₃	—	10	1	no	—
364	C₄×D₃	—	10	1	no	—
365	Dic₆	—	5	4	no	—
366	C₃×C₈	—	2	2	no	—
367	C₃×C₈	—	2	1	no	—
368	C₃×C₈	#711	1	2	yes	complemented
369	C₃⋊C₈	—	5	2	no	—
370	C₃⋊C₈	—	10	1	no	—
371	C₃⋊C₈	—	10	2	no	—
372	C₂²×C₅	—	2	2	no	—
373	C₂²×C₅	—	2	2	no	—
374	C₂²×C₅	C₂×D₃×C₈	1	4	yes	—
375	C₂²×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
376	C₂×D₅	—	3	2	no	—
377	C₂×D₅	—	6	1	no	—
378	C₂×D₅	—	6	1	no	—
379	C₄×C₅	—	2	1	no	—
380	C₄×C₅	—	2	2	no	—
381	C₄×C₅	C₂×D₃×C₈	1	2	yes	—
382	C₄×C₅	C₂×#237	1	1	yes	characteristic
383	C₄×C₅	D₃×#41	1	1	yes	characteristic
384	Dic₅	—	3	4	no	—
385	Dic₅	—	3	2	no	—
386	Dic₅	—	3	2	no	—
387	Dic₅	—	6	2	no	—
388	Dic₅	—	6	1	no	—
389	#41	—	15	8	no	—
390	C₂×Q₈	—	15	1	no	—
391	C₂×D₄	—	15	2	no	—
392	C₂×D₄	C₄×D₁₅	1	1	yes	characteristic
393	C₂²×C₄	—	15	2	no	—
394	C₂²×C₄	—	15	1	no	—
395	C₂²×C₄	—	15	2	no	—
396	C₂²×C₄	—	15	1	no	—
397	C₂²×C₄	—	15	1	no	—
398	C₂²×C₄	C₂²×D₁₅	1	2	yes	—
399	C₂×C₈	—	2	4	no	—
400	C₂×C₈	—	15	1	no	—
401	C₂×C₈	—	15	1	no	—
402	C₂×C₈	—	15	2	no	—
403	C₂×C₈	—	30	2	no	—
404	C₂×C₈	—	30	4	no	—
405	C₂×C₈	—	30	2	no	—
406	C₂×C₈	C₂²×D₁₅	1	2	yes	—
407	C₂×C₈	C₂²×D₁₅	1	1	yes	characteristic
408	C₂×C₈	C₂²×D₁₅	1	1	yes	characteristic
409	C₄⋊C₄	—	15	2	no	—
410	C₄⋊C₄	—	15	2	no	—
411	C₄⋊C₄	—	15	1	no	—
412	C₄⋊C₄	C₄×D₁₅	1	1	yes	characteristic
413	C₂²⋊C₄	—	15	2	no	—
414	C₂²⋊C₄	—	15	2	no	—
415	C₂²⋊C₄	C₄×D₁₅	1	2	yes	—
416	C₄²	—	15	2	no	—
417	C₄²	—	15	1	no	—
418	C₄²	—	15	2	no	—
419	C₄²	—	15	1	no	—
420	C₄²	—	15	1	no	—
421	C₄²	—	15	2	no	—
422	C₄²	C₂²×D₁₅	1	1	yes	characteristic
423	C₃×C₅	C₈×#41	1	1	yes	characteristic, complemented, Hall
424	C₂²×C₃	—	2	2	no	—
425	C₂²×C₃	—	2	2	no	—
426	C₂²×C₃	C₂×C₈×D₅	1	4	yes	—
427	C₂²×C₃	C₂²×C₄×D₅	1	1	yes	characteristic
428	C₂×D₃	—	5	2	no	—
429	C₂×D₃	—	10	1	no	—
430	C₂×D₃	—	10	1	no	—
431	C₃×C₄	—	2	1	no	—
432	C₃×C₄	—	2	2	no	—
433	C₃×C₄	C₂×C₈×D₅	1	2	yes	—
434	C₃×C₄	C₂×#711	1	1	yes	characteristic
435	C₃×C₄	D₅×#41	1	1	yes	characteristic
436	Dic₃	—	5	4	no	—
437	Dic₃	—	5	2	no	—
438	Dic₃	—	5	2	no	—
439	Dic₃	—	10	2	no	—
440	Dic₃	—	10	1	no	—
441	C₂×C₅	—	2	4	no	—
442	C₂×C₅	C₄×#237	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	2	no	—
446	C₂³	—	15	1	no	—
447	C₂³	C₂×C₄×D₁₅	1	2	yes	—
448	Q₈	—	15	4	no	—
449	D₄	—	15	8	no	—
450	D₄	C₈×D₁₅	1	4	yes	complemented
451	C₂×C₄	—	2	2	no	—
452	C₂×C₄	—	2	2	no	—
453	C₂×C₄	—	15	8	no	—
454	C₂×C₄	—	15	1	no	—
455	C₂×C₄	—	15	1	no	—
456	C₂×C₄	—	15	2	no	—
457	C₂×C₄	—	15	4	no	—
458	C₂×C₄	—	15	1	no	—
459	C₂×C₄	—	15	2	no	—
460	C₂×C₄	—	30	2	no	—
461	C₂×C₄	—	30	4	no	—
462	C₂×C₄	—	30	1	no	—
463	C₂×C₄	—	30	1	no	—
464	C₂×C₄	C₂×C₄×D₁₅	1	2	yes	—
465	C₂×C₄	C₂×C₄×D₁₅	1	1	yes	characteristic
466	C₂×C₄	C₂×C₄×D₁₅	1	1	yes	characteristic
467	C₂×C₄	C₂³×D₁₅	1	1	yes	characteristic
468	C₈	—	2	2	no	—
469	C₈	—	2	1	no	—
470	C₈	—	15	2	no	—
471	C₈	—	30	1	no	—
472	C₈	—	30	2	no	—
473	C₈	#6819	1	2	yes	direct product factor
474	C₂×C₃	—	2	4	no	—
475	C₂×C₃	C₄×#711	1	1	yes	characteristic
476	C₂×C₃	C₂²×C₈×D₅	1	1	yes	characteristic
477	C₂×C₃	D₅×#131	1	1	yes	characteristic
478	D₃	—	10	2	no	—
479	C₅	C₈×#237	1	1	yes	characteristic, complemented, Sylow
480	C₂²	—	2	2	no	—
481	C₂²	—	2	2	no	—
482	C₂²	—	15	2	no	—
483	C₂²	—	30	1	no	—
484	C₂²	—	30	1	no	—
485	C₂²	C₂×C₈×D₁₅	1	4	yes	—
486	C₂²	C₂²×C₄×D₁₅	1	1	yes	characteristic
487	C₄	—	2	2	no	—
488	C₄	—	2	1	no	—
489	C₄	—	15	2	no	—
490	C₄	—	15	4	no	—
491	C₄	—	15	2	no	—
492	C₄	—	30	1	no	—
493	C₄	—	30	2	no	—
494	C₄	C₂×C₈×D₁₅	1	2	yes	—
495	C₄	C₂×#6819	1	1	yes	characteristic
496	C₄	#41×D₁₅	1	1	yes	characteristic
497	C₃	C₈×#711	1	1	yes	characteristic, complemented, Sylow
498	C₂	—	2	4	no	—
499	C₂	—	30	2	no	—
500	C₂	C₄×#6819	1	1	yes	characteristic
501	C₂	C₂²×C₈×D₁₅	1	1	yes	characteristic
502	C₂	D₁₅×#131	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₈	C₂²×D₁₅
commutator	C₂×C₃×C₅	C₂³×C₈
Frattini	C₂×C₄	C₂³×D₁₅
Fitting	C₃×C₅×C₈×D₄	C₂
socle	C₂²×C₃×C₅	C₂³×C₄
prime radical	C₂×#6819	C₄
cosocle	C₂×C₃×C₄×C₅	C₂⁴
hypercenter	C₈×D₄	D₁₅
hypocenter	C₃×C₅	C₈×#41
LCS	G ▷ C₂×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂×C₈ ◁ C₈×D₄

Complements

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

N	H ≅ G/N	type
2. C₃×C₅×C₈×D₄	C₂	semidirect
3. C₈×#1220	C₂	semidirect
4. C₂×C₈×Dic₁₅	C₂	semidirect
5. D₄×C₃⋊#168	C₂	semidirect
6. #11750934	C₂	semidirect
7. #11750931	C₂	semidirect
8. #11750826	C₂	semidirect
9. #11750819	C₂	semidirect
10. C₄×C₈×D₁₅	C₂	semidirect
11. C₈×Dic₃₀	C₂	semidirect
44. C₅×C₈×D₄	D₃	semidirect
59. #6819	C₈	direct (N × H)
89. C₃×C₈×D₄	D₅	semidirect
131. C₃×C₅×D₄	C₂×C₈	semidirect
138. #1220	C₂×C₈	semidirect
140. C₂×Dic₁₅	C₂×C₈	semidirect
149. C₄×D₁₅	C₂×C₈	semidirect
150. Dic₃₀	C₂×C₈	semidirect
153. C₃×C₅×C₈	#41	semidirect
156. C₃⋊#168	#41	semidirect
226. C₈×D₄	D₁₅	semidirect
284. C₅×D₄	D₃×C₈	semidirect
306. C₅×C₈	#237	semidirect
346. C₃×D₄	C₈×D₅	semidirect
368. C₃×C₈	#711	semidirect
423. C₃×C₅	C₈×#41	semidirect
450. D₄	C₈×D₁₅	semidirect
473. C₈	#6819	direct (N × H)
479. C₅	C₈×#237	semidirect
497. C₃	C₈×#711	semidirect

Maximal subgroups

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

subgroup	index
C₄×#6819	2
C₃×C₅×C₈×D₄	2
C₈×#1220	2
C₂×C₈×Dic₁₅	2
D₄×C₃⋊#168	2
#11750934	2
#11750931	2
#11750826	2
#11750819	2
C₄×C₈×D₁₅	2
C₈×Dic₃₀	2
C₈×#711	3
C₈×#237	5

Subgroups — C8×#6819 #14418886

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈×#6819 #14418886