Subgroups — C₂×C₈×D₅×Dic₃ #14411173

Order 1920.

1520 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×C₈×D₅	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×D₅×Dic₃	C₂	1	1	yes	maximal, characteristic
3	C₂²×D₅×C₃⋊C₈	C₂	1	1	yes	maximal, characteristic
4	C₂×C₈×Dic₁₅	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₅×C₈×Dic₃	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#90951	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×Dic₃×#168	C₂	1	1	yes	maximal, characteristic, complemented
8	C₈×D₅×Dic₃	C₂	1	8	yes	maximal, direct product factor
9	C₂×C₄×C₈×D₅	—	3	1	no	maximal, Hall
10	C₂²×C₃×C₄×D₅	C₂²	1	1	yes	characteristic
11	C₂²×D₅×Dic₃	C₄	1	2	yes	—
12	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
13	C₂×C₄×Dic₁₅	C₂²	1	1	yes	characteristic
14	C₂²×C₃⋊#168	C₂²	1	1	yes	characteristic
15	C₂×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic
16	C₂²×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic
17	C₂²×C₃×#168	C₂²	1	1	yes	characteristic
18	C₂×C₃×C₈×D₅	C₄	1	8	yes	complemented
19	C₂×C₃×C₈×D₅	C₂²	1	4	yes	—
20	C₂×Dic₃×Dic₅	C₄	1	2	yes	—
21	C₄×D₅×Dic₃	C₄	1	4	yes	—
22	C₄×D₅×Dic₃	C₂²	1	4	yes	—
23	C₂×D₅×C₃⋊C₈	C₄	1	8	yes	complemented
24	C₂×D₅×C₃⋊C₈	C₂²	1	4	yes	—
25	C₈×Dic₁₅	C₂²	1	4	yes	complemented
26	C₅×C₈×Dic₃	C₂²	1	4	yes	complemented
27	#90951	C₂²	1	4	yes	complemented
28	Dic₃×#168	C₂²	1	4	yes	complemented
29	C₂²×C₈×Dic₃	—	5	1	no	maximal, Hall
30	C₂²×C₈×D₅	—	3	1	no	—
31	C₂²×C₈×D₅	D₃	1	1	yes	characteristic
32	C₂×C₄²×D₅	—	3	1	no	—
33	C₂×C₄×C₅×C₈	—	3	1	no	—
34	C₂×C₈×Dic₅	—	3	1	no	—
35	C₂×C₈×Dic₅	—	3	1	no	—
36	C₂×C₄×#168	—	3	1	no	—
37	C₄×C₈×D₅	—	3	8	no	—
38	C₂³×C₃×D₅	C₂×C₄	1	1	yes	characteristic
39	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
40	C₂²×Dic₁₅	C₂×C₄	1	2	yes	—
41	C₂²×C₅×Dic₃	C₂×C₄	1	2	yes	—
42	C₂²×C₃×Dic₅	C₂×C₄	1	1	yes	characteristic
43	C₂×C₃×C₄×D₅	C₂×C₄	1	2	yes	—
44	C₂×C₃×C₄×D₅	C₂×C₄	1	4	yes	—
45	C₂×C₃×C₄×D₅	C₂×C₄	1	4	yes	—
46	C₂×C₃×C₄×D₅	C₂³	1	2	yes	—
47	C₂×D₅×Dic₃	C₈	1	16	yes	direct product factor
48	C₂×D₅×Dic₃	C₂×C₄	1	8	yes	—
49	C₂×C₃×C₅×C₈	C₂×C₄	1	4	yes	complemented
50	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
51	C₄×Dic₁₅	C₂×C₄	1	2	yes	—
52	C₄×Dic₁₅	C₂³	1	2	yes	—
53	C₂×C₃⋊#168	C₂×C₄	1	4	yes	complemented
54	C₂×C₃⋊#168	C₂³	1	2	yes	—
55	C₄×C₅×Dic₃	C₂×C₄	1	2	yes	—
56	C₄×C₅×Dic₃	C₂³	1	2	yes	—
57	C₂×C₅×C₃⋊C₈	C₂×C₄	1	4	yes	complemented
58	C₂×C₅×C₃⋊C₈	C₂³	1	2	yes	—
59	C₂×C₃×#168	C₂×C₄	1	4	yes	complemented
60	C₂×C₃×#168	C₂³	1	2	yes	—
61	C₃×C₈×D₅	C₂×C₄	1	16	yes	complemented
62	Dic₃×Dic₅	C₂×C₄	1	8	yes	—
63	D₅×C₃⋊C₈	C₂×C₄	1	16	yes	complemented
64	C₂³×C₃×C₈	—	5	1	no	—
65	C₂²×C₄×Dic₃	—	5	1	no	—
66	C₂³×C₃⋊C₈	—	5	1	no	—
67	C₂×C₈×Dic₃	—	5	1	no	—
68	C₂×C₈×Dic₃	—	5	1	no	—
69	C₂×C₈×Dic₃	—	5	1	no	—
70	C₂×C₈×Dic₃	—	5	8	no	—
71	C₂×C₈×Dic₃	D₅	1	1	yes	characteristic, direct product factor
72	C₂²×C₄×D₅	—	3	2	no	—
73	C₂²×C₄×D₅	C₂×D₃	1	1	yes	characteristic
74	C₂²×C₅×C₈	—	3	1	no	—
75	C₂²×C₅×C₈	C₂×D₃	1	1	yes	characteristic
76	C₂×C₄²×C₅	—	3	1	no	—
77	C₂×C₄×Dic₅	—	3	1	no	—
78	C₂×C₄×Dic₅	—	3	2	no	—
79	C₂²×#168	—	3	1	no	—
80	C₂²×#168	C₂×D₃	1	1	yes	characteristic
81	C₂×C₈×D₅	—	3	8	no	—
82	C₂×C₈×D₅	—	3	4	no	—
83	C₂×C₈×D₅	Dic₃	1	8	yes	direct product factor
84	C₂×C₈×D₅	C₂×D₃	1	4	yes	—
85	C₄²×D₅	—	3	4	no	—
86	C₄²×D₅	—	3	4	no	—
87	C₄×C₅×C₈	—	3	4	no	—
88	C₈×Dic₅	—	3	4	no	—
89	C₈×Dic₅	—	3	4	no	—
90	C₄×#168	—	3	4	no	—
91	C₂²×C₄×C₈	—	15	1	no	Sylow
92	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
93	C₂²×C₃×D₅	C₄²	1	4	yes	—
94	C₂²×C₃×D₅	C₂×C₈	1	8	yes	—
95	C₂²×C₃×D₅	C₂²×C₄	1	2	yes	—
96	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
97	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
98	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
99	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
100	C₂×Dic₁₅	C₂×C₈	1	8	yes	complemented
101	C₂×Dic₁₅	C₂²×C₄	1	4	yes	—
102	C₂×C₅×Dic₃	C₂×C₈	1	8	yes	complemented
103	C₂×C₅×Dic₃	C₂²×C₄	1	4	yes	—
104	C₂×C₃×Dic₅	C₄²	1	4	yes	—
105	C₂×C₃×Dic₅	C₂²×C₄	1	2	yes	—
106	C₃×C₄×D₅	C₄²	1	8	yes	—
107	C₃×C₄×D₅	C₂²×C₄	1	4	yes	—
108	C₃×C₄×D₅	C₂²×C₄	1	4	yes	—
109	D₅×Dic₃	C₂×C₈	1	32	yes	direct product factor
110	C₃×C₅×C₈	C₂²×C₄	1	4	yes	complemented
111	C₃⋊#168	C₂²×C₄	1	4	yes	complemented
112	C₃×#168	C₂²×C₄	1	4	yes	complemented
113	C₅×C₃⋊C₈	C₂²×C₄	1	4	yes	complemented
114	C₂³×C₃×C₄	—	5	1	no	—
115	C₂³×Dic₃	—	5	2	no	—
116	C₂²×C₃×C₈	—	5	1	no	—
117	C₂²×C₃×C₈	—	5	8	no	—
118	C₂²×C₃×C₈	—	5	4	no	—
119	C₂²×C₃×C₈	C₂×D₅	1	1	yes	characteristic
120	C₂×C₄×Dic₃	—	5	1	no	—
121	C₂×C₄×Dic₃	—	5	2	no	—
122	C₂×C₄×Dic₃	—	5	4	no	—
123	C₂×C₄×Dic₃	—	5	4	no	—
124	C₂×C₄×Dic₃	C₂×D₅	1	1	yes	characteristic
125	C₂²×C₃⋊C₈	—	5	1	no	—
126	C₂²×C₃⋊C₈	—	5	8	no	—
127	C₂²×C₃⋊C₈	—	5	4	no	—
128	C₂²×C₃⋊C₈	C₂×D₅	1	1	yes	characteristic
129	C₈×Dic₃	—	5	4	no	—
130	C₈×Dic₃	—	5	4	no	—
131	C₈×Dic₃	—	5	4	no	—
132	C₈×Dic₃	C₂×D₅	1	4	yes	direct product factor
133	C₂³×D₅	C₄×D₃	1	1	yes	characteristic
134	C₂²×C₄×C₅	—	3	2	no	—
135	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
136	C₂²×Dic₅	—	3	2	no	—
137	C₂²×Dic₅	C₄×D₃	1	1	yes	characteristic
138	C₂×C₄×D₅	—	3	16	no	—
139	C₂×C₄×D₅	—	3	8	no	—
140	C₂×C₄×D₅	C₄×D₃	1	2	yes	—
141	C₂×C₄×D₅	C₄×D₃	1	4	yes	—
142	C₂×C₄×D₅	C₂×Dic₃	1	4	yes	—
143	C₂×C₄×D₅	C₂²×D₃	1	2	yes	—
144	C₂×C₅×C₈	—	3	4	no	—
145	C₂×C₅×C₈	—	3	2	no	—
146	C₂×C₅×C₈	C₂×Dic₃	1	4	yes	complemented
147	C₂×C₅×C₈	C₂²×D₃	1	2	yes	—
148	C₄²×C₅	—	3	2	no	—
149	C₄²×C₅	—	3	2	no	—
150	C₄×Dic₅	—	3	2	no	—
151	C₄×Dic₅	—	3	2	no	—
152	C₄×Dic₅	—	3	8	no	—
153	C₂×#168	—	3	4	no	—
154	C₂×#168	—	3	2	no	—
155	C₂×#168	C₂×Dic₃	1	4	yes	complemented
156	C₂×#168	C₂²×D₃	1	2	yes	—
157	C₈×D₅	—	3	16	no	—
158	C₈×D₅	C₂×Dic₃	1	16	yes	direct product factor
159	C₂³×C₈	—	5	1	no	—
160	C₂³×C₈	—	15	1	no	—
161	C₂²×C₄²	—	15	1	no	—
162	C₂×C₄×C₈	—	3	1	no	—
163	C₂×C₄×C₈	—	15	8	no	—
164	C₂×C₄×C₈	—	15	1	no	—
165	C₂×C₄×C₈	—	15	1	no	—
166	C₂×C₄×C₈	—	15	1	no	—
167	C₂²×C₃×C₅	C₂×C₄²	1	2	yes	—
168	C₂²×C₃×C₅	C₂²×C₈	1	4	yes	—
169	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
170	C₂×C₃×D₅	C₄×C₈	1	16	yes	complemented
171	C₂×C₃×D₅	C₂×C₄²	1	4	yes	—
172	C₂×C₃×D₅	C₂²×C₈	1	8	yes	—
173	C₃×C₄×C₅	C₂×C₄²	1	2	yes	—
174	C₃×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
175	C₃×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
176	Dic₁₅	C₂²×C₈	1	8	yes	complemented
177	C₃×Dic₅	C₂×C₄²	1	4	yes	—
178	C₅×Dic₃	C₂²×C₈	1	8	yes	complemented
179	C₂⁴×C₃	—	5	1	no	—
180	C₂²×C₃×C₄	—	5	1	no	—
181	C₂²×C₃×C₄	—	5	4	no	—
182	C₂²×C₃×C₄	—	5	2	no	—
183	C₂²×C₃×C₄	—	5	4	no	—
184	C₂²×C₃×C₄	—	5	2	no	—
185	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
186	C₂²×Dic₃	—	5	2	no	—
187	C₂²×Dic₃	—	5	16	no	—
188	C₂²×Dic₃	—	5	8	no	—
189	C₂²×Dic₃	C₄×D₅	1	2	yes	—
190	C₂×C₃×C₈	—	5	4	no	—
191	C₂×C₃×C₈	—	5	2	no	—
192	C₂×C₃×C₈	—	5	16	no	—
193	C₂×C₃×C₈	C₄×D₅	1	4	yes	complemented
194	C₂×C₃×C₈	C₂²×D₅	1	2	yes	—
195	C₄×Dic₃	—	5	2	no	—
196	C₄×Dic₃	—	5	2	no	—
197	C₄×Dic₃	—	5	8	no	—
198	C₄×Dic₃	C₄×D₅	1	2	yes	—
199	C₄×Dic₃	C₂²×D₅	1	2	yes	—
200	C₂×C₃⋊C₈	—	5	4	no	—
201	C₂×C₃⋊C₈	—	5	2	no	—
202	C₂×C₃⋊C₈	—	5	16	no	—
203	C₂×C₃⋊C₈	C₄×D₅	1	4	yes	complemented
204	C₂×C₃⋊C₈	C₂²×D₅	1	2	yes	—
205	C₂³×C₅	C₂×C₄×D₃	1	1	yes	characteristic
206	C₂²×D₅	D₃×C₈	1	8	yes	—
207	C₂²×D₅	C₄×Dic₃	1	4	yes	—
208	C₂²×D₅	C₂×C₄×D₃	1	2	yes	—
209	C₂×C₄×C₅	—	3	8	no	—
210	C₂×C₄×C₅	—	3	4	no	—
211	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
212	C₂×C₄×C₅	C₂×C₄×D₃	1	2	yes	—
213	C₂×C₄×C₅	C₂²×Dic₃	1	2	yes	—
214	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
215	C₂×Dic₅	—	3	8	no	—
216	C₂×Dic₅	—	3	4	no	—
217	C₂×Dic₅	C₄×Dic₃	1	4	yes	—
218	C₂×Dic₅	C₂×C₄×D₃	1	2	yes	—
219	C₄×D₅	—	3	32	no	—
220	C₄×D₅	C₄×Dic₃	1	8	yes	—
221	C₄×D₅	C₂×C₄×D₃	1	4	yes	—
222	C₄×D₅	C₂²×Dic₃	1	4	yes	—
223	C₅×C₈	—	3	4	no	—
224	C₅×C₈	C₂²×Dic₃	1	4	yes	complemented
225	#168	—	3	4	no	—
226	#168	C₂²×Dic₃	1	4	yes	complemented
227	C₂³×C₄	—	5	1	no	—
228	C₂³×C₄	—	15	2	no	—
229	C₂²×C₈	—	3	1	no	—
230	C₂²×C₈	—	5	1	no	—
231	C₂²×C₈	—	5	8	no	—
232	C₂²×C₈	—	5	4	no	—
233	C₂²×C₈	—	15	4	no	—
234	C₂²×C₈	—	15	8	no	—
235	C₂²×C₈	—	15	1	no	—
236	C₂²×C₈	D₃×D₅	1	1	yes	characteristic
237	C₂×C₄²	—	3	1	no	—
238	C₂×C₄²	—	15	4	no	—
239	C₂×C₄²	—	15	4	no	—
240	C₂×C₄²	—	15	2	no	—
241	C₂×C₄²	—	15	1	no	—
242	C₄×C₈	—	3	4	no	—
243	C₄×C₈	—	15	4	no	—
244	C₄×C₈	—	15	4	no	—
245	C₄×C₈	—	15	4	no	—
246	C₂×C₃×C₅	C₂×C₄×C₈	1	4	yes	complemented
247	C₂×C₃×C₅	C₂²×C₄²	1	1	yes	characteristic
248	C₂×C₃×C₅	C₂³×C₈	1	2	yes	—
249	C₃×D₅	C₂×C₄×C₈	1	8	yes	complemented
250	C₂³×C₃	—	5	2	no	—
251	C₂³×C₃	—	5	4	no	—
252	C₂³×C₃	—	5	8	no	—
253	C₂³×C₃	C₂×C₄×D₅	1	1	yes	characteristic
254	C₂×C₃×C₄	—	5	2	no	—
255	C₂×C₃×C₄	—	5	4	no	—
256	C₂×C₃×C₄	—	5	4	no	—
257	C₂×C₃×C₄	—	5	4	no	—
258	C₂×C₃×C₄	—	5	8	no	—
259	C₂×C₃×C₄	C₂×C₄×D₅	1	2	yes	—
260	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
261	C₂×C₃×C₄	C₂×C₄×D₅	1	2	yes	—
262	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
263	C₂×Dic₃	—	5	4	no	—
264	C₂×Dic₃	—	5	8	no	—
265	C₂×Dic₃	—	5	32	no	—
266	C₂×Dic₃	C₈×D₅	1	8	yes	direct product factor
267	C₂×Dic₃	C₂×C₄×D₅	1	4	yes	—
268	C₃×C₈	—	5	4	no	—
269	C₃×C₈	C₂×C₄×D₅	1	4	yes	complemented
270	C₃⋊C₈	—	5	4	no	—
271	C₃⋊C₈	C₂×C₄×D₅	1	4	yes	complemented
272	C₂²×C₅	C₂×D₃×C₈	1	4	yes	—
273	C₂²×C₅	C₂×C₄×Dic₃	1	2	yes	—
274	C₂²×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
275	C₂×D₅	C₈×Dic₃	1	16	yes	direct product factor
276	C₂×D₅	C₂×D₃×C₈	1	8	yes	—
277	C₂×D₅	C₂×C₄×Dic₃	1	4	yes	—
278	C₄×C₅	—	3	8	no	—
279	C₄×C₅	C₂×C₄×Dic₃	1	2	yes	—
280	C₄×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
281	C₄×C₅	C₂³×Dic₃	1	1	yes	characteristic
282	Dic₅	—	3	8	no	—
283	Dic₅	C₂×C₄×Dic₃	1	4	yes	—
284	C₂⁴	—	5	1	no	—
285	C₂²×C₄	—	3	2	no	—
286	C₂²×C₄	—	5	1	no	—
287	C₂²×C₄	—	5	2	no	—
288	C₂²×C₄	—	5	4	no	—
289	C₂²×C₄	—	5	4	no	—
290	C₂²×C₄	—	5	2	no	—
291	C₂²×C₄	—	15	8	no	—
292	C₂²×C₄	—	15	16	no	—
293	C₂²×C₄	—	15	2	no	—
294	C₂²×C₄	C₂×D₃×D₅	1	1	yes	characteristic
295	C₂×C₈	—	3	4	no	—
296	C₂×C₈	—	3	2	no	—
297	C₂×C₈	—	5	4	no	—
298	C₂×C₈	—	5	2	no	—
299	C₂×C₈	—	5	16	no	—
300	C₂×C₈	—	15	16	no	—
301	C₂×C₈	—	15	4	no	—
302	C₂×C₈	—	15	2	no	—
303	C₂×C₈	D₅×Dic₃	1	4	yes	direct product factor
304	C₂×C₈	C₂×D₃×D₅	1	2	yes	—
305	C₄²	—	3	2	no	—
306	C₄²	—	3	2	no	—
307	C₄²	—	15	8	no	—
308	C₄²	—	15	2	no	—
309	C₄²	—	15	2	no	—
310	C₃×C₅	C₂²×C₄×C₈	1	1	yes	characteristic, complemented, Hall
311	C₂²×C₃	—	5	4	no	—
312	C₂²×C₃	—	5	8	no	—
313	C₂²×C₃	—	5	16	no	—
314	C₂²×C₃	C₄²×D₅	1	2	yes	—
315	C₂²×C₃	C₂×C₈×D₅	1	4	yes	—
316	C₂²×C₃	C₂²×C₄×D₅	1	1	yes	characteristic
317	C₃×C₄	—	5	4	no	—
318	C₃×C₄	C₄²×D₅	1	2	yes	—
319	C₃×C₄	C₂²×C₄×D₅	1	1	yes	characteristic
320	C₃×C₄	C₂²×C₄×D₅	1	1	yes	characteristic
321	Dic₃	—	5	8	no	—
322	Dic₃	C₂×C₈×D₅	1	8	yes	direct product factor
323	C₂×C₅	C₂×C₈×Dic₃	1	4	yes	complemented
324	C₂×C₅	C₂²×D₃×C₈	1	2	yes	—
325	C₂×C₅	C₂²×C₄×Dic₃	1	1	yes	characteristic
326	D₅	C₂×C₈×Dic₃	1	8	yes	direct product factor
327	C₂³	—	5	2	no	—
328	C₂³	—	5	8	no	—
329	C₂³	—	5	4	no	—
330	C₂³	C₄×D₃×D₅	1	1	yes	characteristic
331	C₂×C₄	—	3	4	no	—
332	C₂×C₄	—	3	8	no	—
333	C₂×C₄	—	5	2	no	—
334	C₂×C₄	—	5	4	no	—
335	C₂×C₄	—	5	4	no	—
336	C₂×C₄	—	5	4	no	—
337	C₂×C₄	—	5	8	no	—
338	C₂×C₄	—	15	32	no	—
339	C₂×C₄	—	15	4	no	—
340	C₂×C₄	—	15	8	no	—
341	C₂×C₄	C₄×D₃×D₅	1	2	yes	—
342	C₂×C₄	C₄×D₃×D₅	1	1	yes	characteristic
343	C₂×C₄	C₂×D₅×Dic₃	1	2	yes	—
344	C₂×C₄	C₂²×D₃×D₅	1	1	yes	characteristic
345	C₈	—	3	4	no	—
346	C₈	—	5	4	no	—
347	C₈	—	15	4	no	—
348	C₈	C₂×D₅×Dic₃	1	4	yes	direct product factor
349	C₂×C₃	—	5	8	no	—
350	C₂×C₃	C₄×C₈×D₅	1	4	yes	complemented
351	C₂×C₃	C₂×C₄²×D₅	1	1	yes	characteristic
352	C₂×C₃	C₂²×C₈×D₅	1	2	yes	—
353	C₅	C₂²×C₈×Dic₃	1	1	yes	characteristic, complemented, Sylow
354	C₂²	—	5	4	no	—
355	C₂²	—	5	8	no	—
356	C₂²	—	5	16	no	—
357	C₂²	D₃×C₈×D₅	1	4	yes	—
358	C₂²	C₄×D₅×Dic₃	1	2	yes	—
359	C₂²	C₂×C₄×D₃×D₅	1	1	yes	characteristic
360	C₄	—	3	8	no	—
361	C₄	—	5	4	no	—
362	C₄	—	15	8	no	—
363	C₄	C₄×D₅×Dic₃	1	2	yes	—
364	C₄	C₂×C₄×D₃×D₅	1	1	yes	characteristic
365	C₄	C₂²×D₅×Dic₃	1	1	yes	characteristic
366	C₃	C₂×C₄×C₈×D₅	1	1	yes	characteristic, complemented, Sylow
367	C₂	—	5	8	no	—
368	C₂	C₈×D₅×Dic₃	1	4	yes	direct product factor
369	C₂	C₂×D₃×C₈×D₅	1	2	yes	—
370	C₂	C₂×C₄×D₅×Dic₃	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
4. C₂×C₈×Dic₁₅	C₂	semidirect
5. C₂×C₅×C₈×Dic₃	C₂	semidirect
6. C₂×#90951	C₂	semidirect
7. C₂×Dic₃×#168	C₂	semidirect
8. C₈×D₅×Dic₃	C₂	direct (N × H)
18. C₂×C₃×C₈×D₅	C₄	semidirect
23. C₂×D₅×C₃⋊C₈	C₄	semidirect
25. C₈×Dic₁₅	C₂²	semidirect
26. C₅×C₈×Dic₃	C₂²	semidirect
27. #90951	C₂²	semidirect
28. Dic₃×#168	C₂²	semidirect
47. C₂×D₅×Dic₃	C₈	direct (N × H)
49. C₂×C₃×C₅×C₈	C₂×C₄	semidirect
53. C₂×C₃⋊#168	C₂×C₄	semidirect
57. C₂×C₅×C₃⋊C₈	C₂×C₄	semidirect
59. C₂×C₃×#168	C₂×C₄	semidirect
61. C₃×C₈×D₅	C₂×C₄	semidirect
63. D₅×C₃⋊C₈	C₂×C₄	semidirect
71. C₂×C₈×Dic₃	D₅	direct (N × H)
83. C₂×C₈×D₅	Dic₃	direct (N × H)
100. C₂×Dic₁₅	C₂×C₈	semidirect
102. C₂×C₅×Dic₃	C₂×C₈	semidirect
109. D₅×Dic₃	C₂×C₈	direct (N × H)
110. C₃×C₅×C₈	C₂²×C₄	semidirect
111. C₃⋊#168	C₂²×C₄	semidirect
112. C₃×#168	C₂²×C₄	semidirect
113. C₅×C₃⋊C₈	C₂²×C₄	semidirect
132. C₈×Dic₃	C₂×D₅	direct (N × H)
146. C₂×C₅×C₈	C₂×Dic₃	semidirect
155. C₂×#168	C₂×Dic₃	semidirect
158. C₈×D₅	C₂×Dic₃	direct (N × H)
170. C₂×C₃×D₅	C₄×C₈	semidirect
176. Dic₁₅	C₂²×C₈	semidirect
178. C₅×Dic₃	C₂²×C₈	semidirect
193. C₂×C₃×C₈	C₄×D₅	semidirect
203. C₂×C₃⋊C₈	C₄×D₅	semidirect
224. C₅×C₈	C₂²×Dic₃	semidirect
226. #168	C₂²×Dic₃	semidirect
246. C₂×C₃×C₅	C₂×C₄×C₈	semidirect
249. C₃×D₅	C₂×C₄×C₈	semidirect
266. C₂×Dic₃	C₈×D₅	direct (N × H)
269. C₃×C₈	C₂×C₄×D₅	semidirect
271. C₃⋊C₈	C₂×C₄×D₅	semidirect
275. C₂×D₅	C₈×Dic₃	direct (N × H)
303. C₂×C₈	D₅×Dic₃	direct (N × H)
310. C₃×C₅	C₂²×C₄×C₈	semidirect
322. Dic₃	C₂×C₈×D₅	direct (N × H)
323. C₂×C₅	C₂×C₈×Dic₃	semidirect
326. D₅	C₂×C₈×Dic₃	direct (N × H)
348. C₈	C₂×D₅×Dic₃	direct (N × H)
350. C₂×C₃	C₄×C₈×D₅	semidirect
353. C₅	C₂²×C₈×Dic₃	semidirect
366. C₃	C₂×C₄×C₈×D₅	semidirect
368. C₂	C₈×D₅×Dic₃	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₃×C₈×D₅	2
C₂×C₄×D₅×Dic₃	2
C₂²×D₅×C₃⋊C₈	2
C₂×C₈×Dic₁₅	2
C₂×C₅×C₈×Dic₃	2
C₂×#90951	2
C₂×Dic₃×#168	2
C₈×D₅×Dic₃	2
C₂×C₄×C₈×D₅	3
C₂²×C₈×Dic₃	5

Subgroups — C2×C8×D5×Dic3 #14411173

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₈×D₅×Dic₃ #14411173