Subgroups — D₃×D₅×C₄⋊C₈ #14412976

Order 1920.

1280 conjugacy classes of subgroups.

The subgroup lattice has 668 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₃×C₈×D₅	C₂	1	2	yes	maximal
2	C₄²×D₃×D₅	C₂	1	1	yes	maximal, characteristic
3	D₁₅×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×D₃×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×D₅×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
6	#11747585	C₂	1	2	yes	maximal, complemented
7	D₃×#3946	C₂	1	2	yes	maximal, complemented
8	D₅×Dic₃⋊C₈	C₂	1	2	yes	maximal, complemented
9	#11747000	C₂	1	1	yes	maximal, characteristic, complemented
10	D₃×C₄⋊#168	C₂	1	1	yes	maximal, characteristic, complemented
11	D₅×C₄⋊(C₃⋊C₈)	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×D₅×C₄⋊C₈	—	3	1	no	maximal, Hall
13	C₂×C₄×D₃×D₅	C₄	1	1	yes	characteristic
14	C₂×C₄×D₃×D₅	C₄	1	1	yes	characteristic
15	C₂×C₄×D₃×D₅	C₂²	1	1	yes	characteristic
16	C₂×C₈×D₁₅	C₂²	1	2	yes	—
17	C₄²×D₁₅	C₂²	1	1	yes	characteristic
18	C₂×C₅×D₃×C₈	C₂²	1	2	yes	—
19	C₄²×C₅×D₃	C₂²	1	1	yes	characteristic
20	C₂×C₃×C₈×D₅	C₂²	1	2	yes	—
21	C₃×C₄²×D₅	C₂²	1	1	yes	characteristic
22	C₄×#1200	C₄	1	1	yes	characteristic
23	C₄×#1200	C₄	1	1	yes	characteristic
24	C₄×#1200	C₂²	1	1	yes	characteristic
25	C₄×D₃×Dic₅	C₄	1	1	yes	characteristic
26	C₄×D₃×Dic₅	C₄	1	1	yes	characteristic
27	C₄×D₃×Dic₅	C₂²	1	1	yes	characteristic
28	C₄×D₅×Dic₃	C₄	1	1	yes	characteristic
29	C₄×D₅×Dic₃	C₄	1	1	yes	characteristic
30	C₄×D₅×Dic₃	C₂²	1	1	yes	characteristic
31	C₂×#6648	C₂²	1	2	yes	—
32	C₂×D₃×#168	C₂²	1	2	yes	—
33	C₂×D₅×C₃⋊C₈	C₂²	1	2	yes	—
34	D₃×C₈×D₅	—	2	8	no	—
35	C₃×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
36	#91098	C₂²	1	2	yes	complemented
37	C₄⋊(C₃⋊#168)	C₂²	1	1	yes	characteristic, complemented
38	C₅×Dic₃⋊C₈	C₂²	1	2	yes	complemented
39	C₅×C₄⋊(C₃⋊C₈)	C₂²	1	1	yes	characteristic, complemented
40	C₃×#3946	C₂²	1	2	yes	complemented
41	C₃×C₄⋊#168	C₂²	1	1	yes	characteristic, complemented
42	Dic₃⋊#168	C₂²	1	2	yes	complemented
43	#90983	C₂²	1	2	yes	complemented
44	#90982	C₂²	1	2	yes	complemented
45	C₂×D₃×C₄⋊C₈	—	5	1	no	maximal, Hall
46	C₂²×C₈×D₅	—	3	2	no	—
47	C₂×C₄²×D₅	—	3	1	no	—
48	C₂×C₅×C₄⋊C₈	—	3	1	no	—
49	C₂×#3946	—	3	2	no	—
50	C₂×C₄⋊#168	—	3	1	no	—
51	D₅×C₄⋊C₈	—	3	2	no	—
52	D₅×C₄⋊C₈	—	3	1	no	—
53	D₅×C₄⋊C₈	—	3	1	no	—
54	D₅×C₄⋊C₈	—	3	2	no	—
55	D₅×C₄⋊C₈	—	3	1	no	—
56	D₅×C₄⋊C₈	D₃	1	1	yes	characteristic, direct product factor
57	C₂²×D₃×D₅	C₂×C₄	1	1	yes	characteristic
58	C₂×C₄×D₁₅	C₂×C₄	1	1	yes	characteristic
59	C₂×C₄×D₁₅	C₂×C₄	1	1	yes	characteristic
60	C₂×C₄×D₁₅	C₂³	1	1	yes	characteristic
61	C₂×C₄×C₅×D₃	C₂×C₄	1	1	yes	characteristic
62	C₂×C₄×C₅×D₃	C₂×C₄	1	1	yes	characteristic
63	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
64	C₂×C₃×C₄×D₅	C₂×C₄	1	1	yes	characteristic
65	C₂×C₃×C₄×D₅	C₂×C₄	1	1	yes	characteristic
66	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
67	C₂×#1200	C₂×C₄	1	1	yes	characteristic
68	C₂×#1200	C₂×C₄	1	1	yes	characteristic
69	C₂×#1200	C₂×C₄	1	1	yes	characteristic
70	C₂×D₃×Dic₅	C₂×C₄	1	1	yes	characteristic
71	C₂×D₃×Dic₅	C₂×C₄	1	1	yes	characteristic
72	C₂×D₃×Dic₅	C₂×C₄	1	1	yes	characteristic
73	C₂×D₅×Dic₃	C₂×C₄	1	1	yes	characteristic
74	C₂×D₅×Dic₃	C₂×C₄	1	1	yes	characteristic
75	C₂×D₅×Dic₃	C₂×C₄	1	1	yes	characteristic
76	C₄×D₃×D₅	—	2	4	no	—
77	C₄×D₃×D₅	C₈	1	8	yes	complemented
78	C₄×D₃×D₅	D₄	1	4	yes	—
79	C₄×D₃×D₅	Q₈	1	4	yes	—
80	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
81	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
82	C₄×Dic₁₅	C₂×C₄	1	1	yes	characteristic
83	C₄×Dic₁₅	C₂×C₄	1	1	yes	characteristic
84	C₄×Dic₁₅	C₂³	1	1	yes	characteristic
85	C₂×C₃⋊#168	C₂³	1	2	yes	—
86	C₈×D₁₅	—	2	4	no	—
87	C₄×C₅×Dic₃	C₂×C₄	1	1	yes	characteristic
88	C₄×C₅×Dic₃	C₂×C₄	1	1	yes	characteristic
89	C₄×C₅×Dic₃	C₂³	1	1	yes	characteristic
90	C₂×C₅×C₃⋊C₈	C₂³	1	2	yes	—
91	C₅×D₃×C₈	—	2	4	no	—
92	C₃×C₄×Dic₅	C₂×C₄	1	1	yes	characteristic
93	C₃×C₄×Dic₅	C₂×C₄	1	1	yes	characteristic
94	C₃×C₄×Dic₅	C₂³	1	1	yes	characteristic
95	C₂×C₃×#168	C₂³	1	2	yes	—
96	C₃×C₈×D₅	—	2	4	no	—
97	Dic₃×Dic₅	C₂×C₄	1	1	yes	characteristic
98	Dic₃×Dic₅	C₂×C₄	1	1	yes	characteristic
99	Dic₃×Dic₅	C₂×C₄	1	1	yes	characteristic
100	Dic₃×Dic₅	C₂×C₄	1	1	yes	characteristic
101	Dic₃×Dic₅	C₂×C₄	1	1	yes	characteristic
102	Dic₃×Dic₅	C₂×C₄	1	1	yes	characteristic
103	#6648	—	2	4	no	—
104	D₃×#168	—	2	4	no	—
105	D₅×C₃⋊C₈	—	2	4	no	—
106	C₂²×D₃×C₈	—	5	2	no	—
107	C₂×C₄²×D₃	—	5	1	no	—
108	C₂×C₃×C₄⋊C₈	—	5	1	no	—
109	C₂×Dic₃⋊C₈	—	5	2	no	—
110	C₂×C₄⋊(C₃⋊C₈)	—	5	1	no	—
111	D₃×C₄⋊C₈	—	5	2	no	—
112	D₃×C₄⋊C₈	—	5	1	no	—
113	D₃×C₄⋊C₈	—	5	1	no	—
114	D₃×C₄⋊C₈	—	5	2	no	—
115	D₃×C₄⋊C₈	—	5	1	no	—
116	D₃×C₄⋊C₈	D₅	1	1	yes	characteristic, direct product factor
117	C₂²×C₄×D₅	—	3	1	no	—
118	C₂²×C₄×D₅	—	3	1	no	—
119	C₂²×C₄×D₅	—	3	1	no	—
120	C₂²×C₅×C₈	—	3	2	no	—
121	C₂×C₄²×C₅	—	3	1	no	—
122	C₂×C₄×Dic₅	—	3	1	no	—
123	C₂×C₄×Dic₅	—	3	1	no	—
124	C₂×C₄×Dic₅	—	3	1	no	—
125	C₂²×#168	—	3	2	no	—
126	C₂×C₈×D₅	—	3	2	no	—
127	C₂×C₈×D₅	—	3	2	no	—
128	C₂×C₈×D₅	—	3	2	no	—
129	C₂×C₈×D₅	—	6	8	no	—
130	C₂×C₈×D₅	C₂×D₃	1	2	yes	—
131	C₄²×D₅	—	3	1	no	—
132	C₄²×D₅	—	3	1	no	—
133	C₄²×D₅	—	3	1	no	—
134	C₄²×D₅	—	3	1	no	—
135	C₄²×D₅	—	3	1	no	—
136	C₄²×D₅	—	3	1	no	—
137	C₄²×D₅	—	3	1	no	—
138	C₄²×D₅	C₂×D₃	1	1	yes	characteristic
139	C₅×C₄⋊C₈	—	3	2	no	—
140	C₅×C₄⋊C₈	—	3	1	no	—
141	C₅×C₄⋊C₈	C₂×D₃	1	1	yes	characteristic, complemented
142	#3946	—	3	2	no	—
143	#3946	—	3	2	no	—
144	#3946	—	3	2	no	—
145	#3946	C₂×D₃	1	2	yes	complemented
146	C₄⋊#168	—	3	1	no	—
147	C₄⋊#168	—	3	2	no	—
148	C₄⋊#168	C₂×D₃	1	1	yes	characteristic, complemented
149	C₂²×C₄⋊C₈	—	15	1	no	Sylow
150	C₂²×D₁₅	C₂²×C₄	1	1	yes	characteristic
151	C₂²×C₅×D₃	C₂²×C₄	1	1	yes	characteristic
152	C₂²×C₃×D₅	C₂²×C₄	1	1	yes	characteristic
153	C₂×D₃×D₅	C₄⋊C₄	1	4	yes	—
154	C₂×D₃×D₅	C₂×C₈	1	4	yes	—
155	C₂×D₃×D₅	M₁₆	1	4	yes	—
156	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
157	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
158	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
159	C₂×Dic₁₅	C₂²×C₄	1	1	yes	characteristic
160	C₂×Dic₁₅	C₂²×C₄	1	1	yes	characteristic
161	C₂×Dic₁₅	C₂²×C₄	1	1	yes	characteristic
162	C₄×D₁₅	—	2	2	no	—
163	C₄×D₁₅	C₂×C₈	1	4	yes	complemented
164	C₄×D₁₅	C₂×D₄	1	2	yes	—
165	C₄×D₁₅	C₂×Q₈	1	2	yes	—
166	C₂×C₅×Dic₃	C₂²×C₄	1	1	yes	characteristic
167	C₂×C₅×Dic₃	C₂²×C₄	1	1	yes	characteristic
168	C₂×C₅×Dic₃	C₂²×C₄	1	1	yes	characteristic
169	C₄×C₅×D₃	—	2	2	no	—
170	C₄×C₅×D₃	C₂×C₈	1	4	yes	complemented
171	C₄×C₅×D₃	C₂×D₄	1	2	yes	—
172	C₄×C₅×D₃	C₂×Q₈	1	2	yes	—
173	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
174	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
175	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
176	C₃×C₄×D₅	—	2	2	no	—
177	C₃×C₄×D₅	C₂×C₈	1	4	yes	complemented
178	C₃×C₄×D₅	C₂×D₄	1	2	yes	—
179	C₃×C₄×D₅	C₂×Q₈	1	2	yes	—
180	#1200	—	2	2	no	—
181	#1200	C₄⋊C₄	1	4	yes	—
182	#1200	C₂×C₈	1	4	yes	complemented
183	D₃×Dic₅	—	2	2	no	—
184	D₃×Dic₅	C₄⋊C₄	1	4	yes	—
185	D₃×Dic₅	C₂×C₈	1	4	yes	complemented
186	D₅×Dic₃	—	2	2	no	—
187	D₅×Dic₃	C₄⋊C₄	1	4	yes	—
188	D₅×Dic₃	C₂×C₈	1	4	yes	complemented
189	C₃×C₅×C₈	—	2	2	no	—
190	C₃⋊#168	—	2	2	no	—
191	C₃×#168	—	2	2	no	—
192	C₅×C₃⋊C₈	—	2	2	no	—
193	C₂²×C₄×D₃	—	5	1	no	—
194	C₂²×C₄×D₃	—	5	1	no	—
195	C₂²×C₄×D₃	—	5	1	no	—
196	C₂²×C₃×C₈	—	5	2	no	—
197	C₂×C₃×C₄²	—	5	1	no	—
198	C₂×C₄×Dic₃	—	5	1	no	—
199	C₂×C₄×Dic₃	—	5	1	no	—
200	C₂×C₄×Dic₃	—	5	1	no	—
201	C₂²×C₃⋊C₈	—	5	2	no	—
202	C₂×D₃×C₈	—	5	2	no	—
203	C₂×D₃×C₈	—	5	2	no	—
204	C₂×D₃×C₈	—	5	2	no	—
205	C₂×D₃×C₈	—	10	8	no	—
206	C₂×D₃×C₈	C₂×D₅	1	2	yes	—
207	C₄²×D₃	—	5	1	no	—
208	C₄²×D₃	—	5	1	no	—
209	C₄²×D₃	—	5	1	no	—
210	C₄²×D₃	—	5	1	no	—
211	C₄²×D₃	—	5	1	no	—
212	C₄²×D₃	—	5	1	no	—
213	C₄²×D₃	—	5	1	no	—
214	C₄²×D₃	C₂×D₅	1	1	yes	characteristic
215	C₃×C₄⋊C₈	—	5	2	no	—
216	C₃×C₄⋊C₈	—	5	1	no	—
217	C₃×C₄⋊C₈	C₂×D₅	1	1	yes	characteristic, complemented
218	Dic₃⋊C₈	—	5	2	no	—
219	Dic₃⋊C₈	—	5	2	no	—
220	Dic₃⋊C₈	—	5	2	no	—
221	Dic₃⋊C₈	C₂×D₅	1	2	yes	complemented
222	C₄⋊(C₃⋊C₈)	—	5	1	no	—
223	C₄⋊(C₃⋊C₈)	—	5	2	no	—
224	C₄⋊(C₃⋊C₈)	C₂×D₅	1	1	yes	characteristic, complemented
225	C₂³×D₅	—	3	1	no	—
226	C₂²×C₄×C₅	—	3	1	no	—
227	C₂²×C₄×C₅	—	3	1	no	—
228	C₂²×C₄×C₅	—	3	1	no	—
229	C₂²×Dic₅	—	3	1	no	—
230	C₂²×Dic₅	—	3	1	no	—
231	C₂²×Dic₅	—	3	1	no	—
232	C₂×C₄×D₅	—	3	1	no	—
233	C₂×C₄×D₅	—	3	1	no	—
234	C₂×C₄×D₅	—	3	1	no	—
235	C₂×C₄×D₅	—	3	1	no	—
236	C₂×C₄×D₅	—	3	1	no	—
237	C₂×C₄×D₅	—	3	1	no	—
238	C₂×C₄×D₅	—	3	8	no	—
239	C₂×C₄×D₅	—	3	4	no	—
240	C₂×C₄×D₅	—	3	4	no	—
241	C₂×C₄×D₅	—	3	1	no	—
242	C₂×C₄×D₅	—	3	1	no	—
243	C₂×C₄×D₅	—	3	1	no	—
244	C₂×C₄×D₅	—	6	4	no	—
245	C₂×C₄×D₅	C₄×D₃	1	1	yes	characteristic
246	C₂×C₄×D₅	C₄×D₃	1	1	yes	characteristic
247	C₂×C₄×D₅	C₂²×D₃	1	1	yes	characteristic
248	C₂×C₅×C₈	—	3	2	no	—
249	C₂×C₅×C₈	—	6	4	no	—
250	C₂×C₅×C₈	C₂²×D₃	1	2	yes	—
251	C₄²×C₅	—	3	1	no	—
252	C₄²×C₅	—	3	1	no	—
253	C₄²×C₅	—	3	1	no	—
254	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
255	C₄×Dic₅	—	3	1	no	—
256	C₄×Dic₅	—	3	1	no	—
257	C₄×Dic₅	—	3	1	no	—
258	C₄×Dic₅	—	3	1	no	—
259	C₄×Dic₅	—	3	1	no	—
260	C₄×Dic₅	—	3	1	no	—
261	C₄×Dic₅	—	3	1	no	—
262	C₄×Dic₅	—	3	1	no	—
263	C₄×Dic₅	—	3	1	no	—
264	C₄×Dic₅	C₄×D₃	1	1	yes	characteristic
265	C₄×Dic₅	C₄×D₃	1	1	yes	characteristic
266	C₄×Dic₅	C₂²×D₃	1	1	yes	characteristic
267	C₂×#168	—	3	2	no	—
268	C₂×#168	—	6	4	no	—
269	C₂×#168	C₂²×D₃	1	2	yes	—
270	C₈×D₅	—	2	4	no	—
271	C₈×D₅	—	6	4	no	—
272	C₈×D₅	—	6	4	no	—
273	C₈×D₅	—	6	4	no	—
274	C₂³×C₈	—	15	2	no	—
275	C₂²×C₄²	—	15	1	no	—
276	C₂×C₄⋊C₈	—	3	1	no	—
277	C₂×C₄⋊C₈	—	5	1	no	—
278	C₂×C₄⋊C₈	—	15	2	no	—
279	C₂×C₄⋊C₈	—	15	1	no	—
280	C₂×C₄⋊C₈	—	15	1	no	—
281	C₂×C₄⋊C₈	—	15	2	no	—
282	C₂×C₄⋊C₈	—	15	1	no	—
283	C₂×C₄⋊C₈	—	15	2	no	—
284	C₂×C₄⋊C₈	—	15	1	no	—
285	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
286	C₂×D₁₅	C₂×C₄⋊C₄	1	2	yes	—
287	C₂×D₁₅	C₂²×C₈	1	2	yes	—
288	C₂×D₁₅	C₂×M₁₆	1	2	yes	—
289	C₂×C₅×D₃	C₂×C₄⋊C₄	1	2	yes	—
290	C₂×C₅×D₃	C₂²×C₈	1	2	yes	—
291	C₂×C₅×D₃	C₂×M₁₆	1	2	yes	—
292	C₂×C₃×D₅	C₂×C₄⋊C₄	1	2	yes	—
293	C₂×C₃×D₅	C₂²×C₈	1	2	yes	—
294	C₂×C₃×D₅	C₂×M₁₆	1	2	yes	—
295	D₃×D₅	C₄⋊C₈	1	16	yes	direct product factor
296	C₃×C₄×C₅	—	2	1	no	—
297	C₃×C₄×C₅	C₂²×C₈	1	2	yes	complemented
298	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
299	C₃×C₄×C₅	C₂²×Q₈	1	1	yes	characteristic
300	Dic₁₅	—	2	1	no	—
301	Dic₁₅	C₂×C₄⋊C₄	1	2	yes	—
302	Dic₁₅	C₂²×C₈	1	2	yes	complemented
303	C₃×Dic₅	—	2	1	no	—
304	C₃×Dic₅	C₂×C₄⋊C₄	1	2	yes	—
305	C₃×Dic₅	C₂²×C₈	1	2	yes	complemented
306	C₅×Dic₃	—	2	1	no	—
307	C₅×Dic₃	C₂×C₄⋊C₄	1	2	yes	—
308	C₅×Dic₃	C₂²×C₈	1	2	yes	complemented
309	C₂³×D₃	—	5	1	no	—
310	C₂²×C₃×C₄	—	5	1	no	—
311	C₂²×C₃×C₄	—	5	1	no	—
312	C₂²×C₃×C₄	—	5	1	no	—
313	C₂²×Dic₃	—	5	1	no	—
314	C₂²×Dic₃	—	5	1	no	—
315	C₂²×Dic₃	—	5	1	no	—
316	C₂×C₄×D₃	—	5	1	no	—
317	C₂×C₄×D₃	—	5	1	no	—
318	C₂×C₄×D₃	—	5	1	no	—
319	C₂×C₄×D₃	—	5	1	no	—
320	C₂×C₄×D₃	—	5	1	no	—
321	C₂×C₄×D₃	—	5	1	no	—
322	C₂×C₄×D₃	—	5	8	no	—
323	C₂×C₄×D₃	—	5	4	no	—
324	C₂×C₄×D₃	—	5	4	no	—
325	C₂×C₄×D₃	—	5	1	no	—
326	C₂×C₄×D₃	—	5	1	no	—
327	C₂×C₄×D₃	—	5	1	no	—
328	C₂×C₄×D₃	—	10	4	no	—
329	C₂×C₄×D₃	C₄×D₅	1	1	yes	characteristic
330	C₂×C₄×D₃	C₄×D₅	1	1	yes	characteristic
331	C₂×C₄×D₃	C₂²×D₅	1	1	yes	characteristic
332	C₂×C₃×C₈	—	5	2	no	—
333	C₂×C₃×C₈	—	10	4	no	—
334	C₂×C₃×C₈	C₂²×D₅	1	2	yes	—
335	C₃×C₄²	—	5	1	no	—
336	C₃×C₄²	—	5	1	no	—
337	C₃×C₄²	—	5	1	no	—
338	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
339	C₄×Dic₃	—	5	1	no	—
340	C₄×Dic₃	—	5	1	no	—
341	C₄×Dic₃	—	5	1	no	—
342	C₄×Dic₃	—	5	1	no	—
343	C₄×Dic₃	—	5	1	no	—
344	C₄×Dic₃	—	5	1	no	—
345	C₄×Dic₃	—	5	1	no	—
346	C₄×Dic₃	—	5	1	no	—
347	C₄×Dic₃	—	5	1	no	—
348	C₄×Dic₃	C₄×D₅	1	1	yes	characteristic
349	C₄×Dic₃	C₄×D₅	1	1	yes	characteristic
350	C₄×Dic₃	C₂²×D₅	1	1	yes	characteristic
351	C₂×C₃⋊C₈	—	5	2	no	—
352	C₂×C₃⋊C₈	—	10	4	no	—
353	C₂×C₃⋊C₈	C₂²×D₅	1	2	yes	—
354	D₃×C₈	—	2	4	no	—
355	D₃×C₈	—	10	4	no	—
356	D₃×C₈	—	10	4	no	—
357	D₃×C₈	—	10	4	no	—
358	C₂³×C₅	—	3	1	no	—
359	C₂²×D₅	—	3	1	no	—
360	C₂²×D₅	—	3	4	no	—
361	C₂²×D₅	—	3	4	no	—
362	C₂²×D₅	—	3	4	no	—
363	C₂²×D₅	C₂×C₄×D₃	1	1	yes	characteristic
364	C₂×C₄×C₅	—	3	1	no	—
365	C₂×C₄×C₅	—	3	1	no	—
366	C₂×C₄×C₅	—	3	4	no	—
367	C₂×C₄×C₅	—	3	2	no	—
368	C₂×C₄×C₅	—	3	2	no	—
369	C₂×C₄×C₅	—	3	1	no	—
370	C₂×C₄×C₅	—	6	2	no	—
371	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
372	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
373	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
374	C₂×Dic₅	—	3	1	no	—
375	C₂×Dic₅	—	3	1	no	—
376	C₂×Dic₅	—	3	4	no	—
377	C₂×Dic₅	—	3	4	no	—
378	C₂×Dic₅	—	3	1	no	—
379	C₂×Dic₅	—	6	2	no	—
380	C₂×Dic₅	C₂×C₄×D₃	1	1	yes	characteristic
381	C₂×Dic₅	C₂×C₄×D₃	1	1	yes	characteristic
382	C₂×Dic₅	C₂×C₄×D₃	1	1	yes	characteristic
383	C₄×D₅	—	2	2	no	—
384	C₄×D₅	—	3	4	no	—
385	C₄×D₅	—	3	4	no	—
386	C₄×D₅	—	3	4	no	—
387	C₄×D₅	—	3	2	no	—
388	C₄×D₅	—	3	2	no	—
389	C₄×D₅	—	3	4	no	—
390	C₄×D₅	—	3	4	no	—
391	C₄×D₅	—	6	2	no	—
392	C₄×D₅	—	6	2	no	—
393	C₄×D₅	—	6	2	no	—
394	C₄×D₅	D₃×C₈	1	4	yes	complemented
395	C₄×D₅	D₃×D₄	1	2	yes	—
396	C₄×D₅	D₃×Q₈	1	2	yes	—
397	C₅×C₈	—	2	2	no	—
398	C₅×C₈	—	6	2	no	—
399	#168	—	2	2	no	—
400	#168	—	6	2	no	—
401	C₂³×C₄	—	15	1	no	—
402	C₂³×C₄	—	15	1	no	—
403	C₂³×C₄	—	15	1	no	—
404	C₂²×C₈	—	3	2	no	—
405	C₂²×C₈	—	5	2	no	—
406	C₂²×C₈	—	15	2	no	—
407	C₂²×C₈	—	15	2	no	—
408	C₂²×C₈	—	15	2	no	—
409	C₂²×C₈	—	15	2	no	—
410	C₂²×C₈	—	30	8	no	—
411	C₂×C₄²	—	3	1	no	—
412	C₂×C₄²	—	5	1	no	—
413	C₂×C₄²	—	15	1	no	—
414	C₂×C₄²	—	15	1	no	—
415	C₂×C₄²	—	15	1	no	—
416	C₂×C₄²	—	15	1	no	—
417	C₂×C₄²	—	15	1	no	—
418	C₂×C₄²	—	15	1	no	—
419	C₂×C₄²	—	15	1	no	—
420	C₂×C₄²	—	15	1	no	—
421	C₂×C₄²	—	15	1	no	—
422	C₂×C₄²	—	15	1	no	—
423	C₄⋊C₈	—	3	2	no	—
424	C₄⋊C₈	—	3	1	no	—
425	C₄⋊C₈	—	5	2	no	—
426	C₄⋊C₈	—	5	1	no	—
427	C₄⋊C₈	—	15	2	no	—
428	C₄⋊C₈	—	15	2	no	—
429	C₄⋊C₈	—	15	2	no	—
430	C₄⋊C₈	—	15	2	no	—
431	C₄⋊C₈	—	15	1	no	—
432	C₄⋊C₈	D₃×D₅	1	1	yes	characteristic, direct product factor
433	C₂×C₃×C₅	C₂²×C₄⋊C₄	1	1	yes	characteristic
434	C₂×C₃×C₅	C₂³×C₈	1	1	yes	characteristic
435	C₂×C₃×C₅	C₂²×M₁₆	1	1	yes	characteristic
436	D₁₅	C₂×C₄⋊C₈	1	4	yes	complemented
437	C₃×D₅	C₂×C₄⋊C₈	1	4	yes	complemented
438	C₅×D₃	C₂×C₄⋊C₈	1	4	yes	complemented
439	C₂³×C₃	—	5	1	no	—
440	C₂²×D₃	—	5	1	no	—
441	C₂²×D₃	—	5	4	no	—
442	C₂²×D₃	—	5	4	no	—
443	C₂²×D₃	—	5	4	no	—
444	C₂²×D₃	C₂×C₄×D₅	1	1	yes	characteristic
445	C₂×C₃×C₄	—	5	1	no	—
446	C₂×C₃×C₄	—	5	1	no	—
447	C₂×C₃×C₄	—	5	2	no	—
448	C₂×C₃×C₄	—	5	2	no	—
449	C₂×C₃×C₄	—	5	4	no	—
450	C₂×C₃×C₄	—	5	1	no	—
451	C₂×C₃×C₄	—	10	2	no	—
452	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
453	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
454	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
455	C₂×Dic₃	—	5	1	no	—
456	C₂×Dic₃	—	5	1	no	—
457	C₂×Dic₃	—	5	4	no	—
458	C₂×Dic₃	—	5	4	no	—
459	C₂×Dic₃	—	5	1	no	—
460	C₂×Dic₃	—	10	2	no	—
461	C₂×Dic₃	C₂×C₄×D₅	1	1	yes	characteristic
462	C₂×Dic₃	C₂×C₄×D₅	1	1	yes	characteristic
463	C₂×Dic₃	C₂×C₄×D₅	1	1	yes	characteristic
464	C₄×D₃	—	2	2	no	—
465	C₄×D₃	—	5	4	no	—
466	C₄×D₃	—	5	4	no	—
467	C₄×D₃	—	5	2	no	—
468	C₄×D₃	—	5	2	no	—
469	C₄×D₃	—	5	4	no	—
470	C₄×D₃	—	5	4	no	—
471	C₄×D₃	—	5	4	no	—
472	C₄×D₃	—	10	2	no	—
473	C₄×D₃	—	10	2	no	—
474	C₄×D₃	—	10	2	no	—
475	C₄×D₃	C₈×D₅	1	4	yes	complemented
476	C₄×D₃	D₄×D₅	1	2	yes	—
477	C₄×D₃	Q₈×D₅	1	2	yes	—
478	C₃×C₈	—	2	2	no	—
479	C₃×C₈	—	10	2	no	—
480	C₃⋊C₈	—	2	2	no	—
481	C₃⋊C₈	—	10	2	no	—
482	C₂²×C₅	—	3	2	no	—
483	C₂²×C₅	—	3	2	no	—
484	C₂²×C₅	—	3	2	no	—
485	C₂²×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
486	C₂×D₅	—	3	2	no	—
487	C₂×D₅	—	3	2	no	—
488	C₂×D₅	—	3	2	no	—
489	C₂×D₅	—	3	16	no	—
490	C₂×D₅	D₃×C₄⋊C₄	1	2	yes	—
491	C₂×D₅	C₂×D₃×C₈	1	2	yes	—
492	C₂×D₅	D₃×M₁₆	1	2	yes	—
493	C₄×C₅	—	2	1	no	—
494	C₄×C₅	—	3	2	no	—
495	C₄×C₅	—	3	2	no	—
496	C₄×C₅	—	6	1	no	—
497	C₄×C₅	C₂×D₃×C₈	1	2	yes	complemented
498	C₄×C₅	C₂×D₃×D₄	1	1	yes	characteristic
499	C₄×C₅	C₂×D₃×Q₈	1	1	yes	characteristic
500	Dic₅	—	2	1	no	—
501	Dic₅	—	3	2	no	—
502	Dic₅	—	3	2	no	—
503	Dic₅	—	6	1	no	—
504	Dic₅	D₃×C₄⋊C₄	1	2	yes	—
505	Dic₅	C₂×D₃×C₈	1	2	yes	complemented
506	C₂⁴	—	15	1	no	—
507	C₂²×C₄	—	3	1	no	—
508	C₂²×C₄	—	3	1	no	—
509	C₂²×C₄	—	3	1	no	—
510	C₂²×C₄	—	5	1	no	—
511	C₂²×C₄	—	5	1	no	—
512	C₂²×C₄	—	5	1	no	—
513	C₂²×C₄	—	15	1	no	—
514	C₂²×C₄	—	15	1	no	—
515	C₂²×C₄	—	15	4	no	—
516	C₂²×C₄	—	15	8	no	—
517	C₂²×C₄	—	15	4	no	—
518	C₂²×C₄	—	15	1	no	—
519	C₂²×C₄	—	15	1	no	—
520	C₂²×C₄	—	15	1	no	—
521	C₂²×C₄	—	15	1	no	—
522	C₂²×C₄	—	15	1	no	—
523	C₂²×C₄	—	15	1	no	—
524	C₂²×C₄	—	15	1	no	—
525	C₂²×C₄	—	15	1	no	—
526	C₂²×C₄	—	15	1	no	—
527	C₂²×C₄	—	15	1	no	—
528	C₂²×C₄	—	30	4	no	—
529	C₂×C₈	—	3	2	no	—
530	C₂×C₈	—	5	2	no	—
531	C₂×C₈	—	6	4	no	—
532	C₂×C₈	—	10	4	no	—
533	C₂×C₈	—	15	2	no	—
534	C₂×C₈	—	30	4	no	—
535	C₂×C₈	—	30	4	no	—
536	C₂×C₈	—	30	4	no	—
537	C₂×C₈	—	30	4	no	—
538	C₂×C₈	C₂×D₃×D₅	1	2	yes	—
539	C₄²	—	3	1	no	—
540	C₄²	—	3	1	no	—
541	C₄²	—	3	1	no	—
542	C₄²	—	5	1	no	—
543	C₄²	—	5	1	no	—
544	C₄²	—	5	1	no	—
545	C₄²	—	15	1	no	—
546	C₄²	—	15	1	no	—
547	C₄²	—	15	1	no	—
548	C₄²	—	15	1	no	—
549	C₄²	—	15	1	no	—
550	C₄²	—	15	1	no	—
551	C₄²	—	15	1	no	—
552	C₄²	—	15	1	no	—
553	C₄²	—	15	1	no	—
554	C₄²	C₂×D₃×D₅	1	1	yes	characteristic
555	C₃×C₅	C₂²×C₄⋊C₈	1	1	yes	characteristic, complemented, Hall
556	C₂²×C₃	—	5	2	no	—
557	C₂²×C₃	—	5	2	no	—
558	C₂²×C₃	—	5	2	no	—
559	C₂²×C₃	C₂²×C₄×D₅	1	1	yes	characteristic
560	C₂×D₃	—	5	2	no	—
561	C₂×D₃	—	5	2	no	—
562	C₂×D₃	—	5	2	no	—
563	C₂×D₃	—	5	16	no	—
564	C₂×D₃	D₅×C₄⋊C₄	1	2	yes	—
565	C₂×D₃	C₂×C₈×D₅	1	2	yes	—
566	C₂×D₃	D₅×M₁₆	1	2	yes	—
567	C₃×C₄	—	2	1	no	—
568	C₃×C₄	—	5	2	no	—
569	C₃×C₄	—	5	2	no	—
570	C₃×C₄	—	10	1	no	—
571	C₃×C₄	C₂×C₈×D₅	1	2	yes	complemented
572	C₃×C₄	C₂×D₄×D₅	1	1	yes	characteristic
573	C₃×C₄	C₂×Q₈×D₅	1	1	yes	characteristic
574	Dic₃	—	2	1	no	—
575	Dic₃	—	5	2	no	—
576	Dic₃	—	5	2	no	—
577	Dic₃	—	10	1	no	—
578	Dic₃	D₅×C₄⋊C₄	1	2	yes	—
579	Dic₃	C₂×C₈×D₅	1	2	yes	complemented
580	C₂×C₅	—	3	4	no	—
581	C₂×C₅	C₂×D₃×C₄⋊C₄	1	1	yes	characteristic
582	C₂×C₅	C₂²×D₃×C₈	1	1	yes	characteristic
583	C₂×C₅	C₂×D₃×M₁₆	1	1	yes	characteristic
584	D₅	—	3	4	no	—
585	D₅	D₃×C₄⋊C₈	1	4	yes	direct product factor
586	C₂³	—	3	1	no	—
587	C₂³	—	5	1	no	—
588	C₂³	—	15	4	no	—
589	C₂³	—	15	4	no	—
590	C₂³	—	15	4	no	—
591	C₂³	—	15	1	no	—
592	C₂×C₄	—	3	1	no	—
593	C₂×C₄	—	3	1	no	—
594	C₂×C₄	—	3	4	no	—
595	C₂×C₄	—	3	2	no	—
596	C₂×C₄	—	3	2	no	—
597	C₂×C₄	—	3	1	no	—
598	C₂×C₄	—	5	1	no	—
599	C₂×C₄	—	5	1	no	—
600	C₂×C₄	—	5	4	no	—
601	C₂×C₄	—	5	2	no	—
602	C₂×C₄	—	5	2	no	—
603	C₂×C₄	—	5	1	no	—
604	C₂×C₄	—	6	2	no	—
605	C₂×C₄	—	10	2	no	—
606	C₂×C₄	—	15	4	no	—
607	C₂×C₄	—	15	4	no	—
608	C₂×C₄	—	15	4	no	—
609	C₂×C₄	—	15	4	no	—
610	C₂×C₄	—	15	4	no	—
611	C₂×C₄	—	15	4	no	—
612	C₂×C₄	—	15	1	no	—
613	C₂×C₄	—	15	1	no	—
614	C₂×C₄	—	15	4	no	—
615	C₂×C₄	—	15	2	no	—
616	C₂×C₄	—	15	2	no	—
617	C₂×C₄	—	15	1	no	—
618	C₂×C₄	—	30	2	no	—
619	C₂×C₄	—	30	2	no	—
620	C₂×C₄	—	30	2	no	—
621	C₂×C₄	—	30	2	no	—
622	C₂×C₄	C₄×D₃×D₅	1	1	yes	characteristic
623	C₂×C₄	C₄×D₃×D₅	1	1	yes	characteristic
624	C₂×C₄	C₂²×D₃×D₅	1	1	yes	characteristic
625	C₈	—	2	2	no	—
626	C₈	—	6	2	no	—
627	C₈	—	10	2	no	—
628	C₈	—	30	2	no	—
629	C₂×C₃	—	5	4	no	—
630	C₂×C₃	C₂×D₅×C₄⋊C₄	1	1	yes	characteristic
631	C₂×C₃	C₂²×C₈×D₅	1	1	yes	characteristic
632	C₂×C₃	C₂×D₅×M₁₆	1	1	yes	characteristic
633	D₃	—	5	4	no	—
634	D₃	D₅×C₄⋊C₈	1	4	yes	direct product factor
635	C₅	C₂×D₃×C₄⋊C₈	1	1	yes	characteristic, complemented, Sylow
636	C₂²	—	3	2	no	—
637	C₂²	—	3	2	no	—
638	C₂²	—	3	2	no	—
639	C₂²	—	5	2	no	—
640	C₂²	—	5	2	no	—
641	C₂²	—	5	2	no	—
642	C₂²	—	15	16	no	—
643	C₂²	—	15	2	no	—
644	C₂²	—	15	2	no	—
645	C₂²	—	15	2	no	—
646	C₂²	C₂×C₄×D₃×D₅	1	1	yes	characteristic
647	C₄	—	2	1	no	—
648	C₄	—	3	2	no	—
649	C₄	—	3	2	no	—
650	C₄	—	5	2	no	—
651	C₄	—	5	2	no	—
652	C₄	—	6	1	no	—
653	C₄	—	10	1	no	—
654	C₄	—	15	2	no	—
655	C₄	—	15	2	no	—
656	C₄	—	30	1	no	—
657	C₄	D₃×C₈×D₅	1	2	yes	complemented
658	C₄	D₃×D₄×D₅	1	1	yes	characteristic
659	C₄	D₃×Q₈×D₅	1	1	yes	characteristic
660	C₃	C₂×D₅×C₄⋊C₈	1	1	yes	characteristic, complemented, Sylow
661	C₂	—	3	4	no	—
662	C₂	—	5	4	no	—
663	C₂	—	15	4	no	—
664	C₂	D₃×D₅×C₄⋊C₄	1	1	yes	characteristic
665	C₂	C₂×D₃×C₈×D₅	1	1	yes	characteristic
666	C₂	D₃×D₅×M₁₆	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
3. D₁₅×C₄⋊C₈	C₂	semidirect
4. C₅×D₃×C₄⋊C₈	C₂	semidirect
5. C₃×D₅×C₄⋊C₈	C₂	semidirect
6. #11747585	C₂	semidirect
7. D₃×#3946	C₂	semidirect
8. D₅×Dic₃⋊C₈	C₂	semidirect
9. #11747000	C₂	semidirect
10. D₃×C₄⋊#168	C₂	semidirect
11. D₅×C₄⋊(C₃⋊C₈)	C₂	semidirect
35. C₃×C₅×C₄⋊C₈	C₂²	semidirect
36. #91098	C₂²	semidirect
37. C₄⋊(C₃⋊#168)	C₂²	semidirect
38. C₅×Dic₃⋊C₈	C₂²	semidirect
39. C₅×C₄⋊(C₃⋊C₈)	C₂²	semidirect
40. C₃×#3946	C₂²	semidirect
41. C₃×C₄⋊#168	C₂²	semidirect
42. Dic₃⋊#168	C₂²	semidirect
43. #90983	C₂²	semidirect
44. #90982	C₂²	semidirect
56. D₅×C₄⋊C₈	D₃	direct (N × H)
77. C₄×D₃×D₅	C₈	semidirect
116. D₃×C₄⋊C₈	D₅	direct (N × H)
141. C₅×C₄⋊C₈	C₂×D₃	semidirect
145. #3946	C₂×D₃	semidirect
148. C₄⋊#168	C₂×D₃	semidirect
163. C₄×D₁₅	C₂×C₈	semidirect
170. C₄×C₅×D₃	C₂×C₈	semidirect
177. C₃×C₄×D₅	C₂×C₈	semidirect
182. #1200	C₂×C₈	semidirect
185. D₃×Dic₅	C₂×C₈	semidirect
188. D₅×Dic₃	C₂×C₈	semidirect
217. C₃×C₄⋊C₈	C₂×D₅	semidirect
221. Dic₃⋊C₈	C₂×D₅	semidirect
224. C₄⋊(C₃⋊C₈)	C₂×D₅	semidirect
295. D₃×D₅	C₄⋊C₈	direct (N × H)
297. C₃×C₄×C₅	C₂²×C₈	semidirect
302. Dic₁₅	C₂²×C₈	semidirect
305. C₃×Dic₅	C₂²×C₈	semidirect
308. C₅×Dic₃	C₂²×C₈	semidirect
394. C₄×D₅	D₃×C₈	semidirect
432. C₄⋊C₈	D₃×D₅	direct (N × H)
436. D₁₅	C₂×C₄⋊C₈	semidirect
437. C₃×D₅	C₂×C₄⋊C₈	semidirect
438. C₅×D₃	C₂×C₄⋊C₈	semidirect
475. C₄×D₃	C₈×D₅	semidirect
497. C₄×C₅	C₂×D₃×C₈	semidirect
505. Dic₅	C₂×D₃×C₈	semidirect
555. C₃×C₅	C₂²×C₄⋊C₈	semidirect
571. C₃×C₄	C₂×C₈×D₅	semidirect
579. Dic₃	C₂×C₈×D₅	semidirect
585. D₅	D₃×C₄⋊C₈	direct (N × H)
634. D₃	D₅×C₄⋊C₈	direct (N × H)
635. C₅	C₂×D₃×C₄⋊C₈	semidirect
657. C₄	D₃×C₈×D₅	semidirect
660. C₃	C₂×D₅×C₄⋊C₈	semidirect

Maximal subgroups

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

subgroup	index
C₂×D₃×C₈×D₅	2
C₄²×D₃×D₅	2
D₁₅×C₄⋊C₈	2
C₅×D₃×C₄⋊C₈	2
C₃×D₅×C₄⋊C₈	2
#11747585	2
D₃×#3946	2
D₅×Dic₃⋊C₈	2
#11747000	2
D₃×C₄⋊#168	2
D₅×C₄⋊(C₃⋊C₈)	2
C₂×D₅×C₄⋊C₈	3
C₂×D₃×C₄⋊C₈	5

Subgroups — D3×D5×C4⋊C8 #14412976

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₃×D₅×C₄⋊C₈ #14412976