Subgroups — C₂×D₃×C₈×Dic₅ #14411175

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

Subgroups — C2×D3×C8×Dic5 #14411175

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×D₃×C₈×Dic₅ #14411175