Subgroups — C₂×D₅×Dic₃⋊C₈ #14412977

Order 1920.

1280 conjugacy classes of subgroups.

The subgroup lattice has 444 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×#91098	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₅×Dic₃⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×Dic₃⋊#168	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#90983	C₂	1	1	yes	maximal, characteristic, complemented
8	D₅×Dic₃⋊C₈	C₂	1	8	yes	maximal, direct product factor
9	C₂×D₅×C₄⋊C₈	—	3	1	no	maximal, Hall
10	C₂²×C₃×C₄×D₅	C₂²	1	1	yes	characteristic
11	C₂²×D₅×Dic₃	C₄	1	1	yes	characteristic
12	C₂²×D₅×Dic₃	C₄	1	1	yes	characteristic
13	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
14	C₂×C₄×Dic₁₅	C₂²	1	1	yes	characteristic
15	C₂²×C₃⋊#168	C₂²	1	1	yes	characteristic
16	C₂×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic
17	C₂²×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic
18	C₂²×C₃×#168	C₂²	1	1	yes	characteristic
19	C₂×C₃×C₈×D₅	—	2	4	no	—
20	C₂×C₃×C₈×D₅	C₂²	1	4	yes	—
21	C₂×Dic₃×Dic₅	C₄	1	1	yes	characteristic
22	C₂×Dic₃×Dic₅	C₄	1	1	yes	characteristic
23	C₄×D₅×Dic₃	C₄	1	4	yes	—
24	C₄×D₅×Dic₃	C₂²	1	4	yes	—
25	C₂×D₅×C₃⋊C₈	—	2	4	no	—
26	C₂×D₅×C₃⋊C₈	C₂²	1	4	yes	—
27	#91098	C₂²	1	4	yes	complemented
28	C₅×Dic₃⋊C₈	C₂²	1	4	yes	complemented
29	Dic₃⋊#168	C₂²	1	4	yes	complemented
30	#90983	C₂²	1	4	yes	complemented
31	C₂²×Dic₃⋊C₈	—	5	1	no	maximal, Hall
32	C₂²×C₈×D₅	—	3	1	no	—
33	C₂²×C₈×D₅	D₃	1	1	yes	characteristic
34	C₂×C₄²×D₅	—	3	1	no	—
35	C₂×C₅×C₄⋊C₈	—	3	1	no	—
36	C₂×#3946	—	3	1	no	—
37	C₂×#3946	—	3	1	no	—
38	C₂×C₄⋊#168	—	3	1	no	—
39	D₅×C₄⋊C₈	—	3	8	no	—
40	C₂³×C₃×D₅	C₂×C₄	1	1	yes	characteristic
41	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
42	C₂²×Dic₁₅	C₂×C₄	1	1	yes	characteristic
43	C₂²×Dic₁₅	C₂×C₄	1	1	yes	characteristic
44	C₂²×C₅×Dic₃	C₂×C₄	1	1	yes	characteristic
45	C₂²×C₅×Dic₃	C₂×C₄	1	1	yes	characteristic
46	C₂²×C₃×Dic₅	C₂×C₄	1	1	yes	characteristic
47	C₂×C₃×C₄×D₅	C₂×C₄	1	2	yes	—
48	C₂×C₃×C₄×D₅	D₄	1	4	yes	—
49	C₂×C₃×C₄×D₅	Q₈	1	4	yes	—
50	C₂×C₃×C₄×D₅	C₂³	1	2	yes	—
51	C₂×D₅×Dic₃	—	2	4	no	—
52	C₂×D₅×Dic₃	C₈	1	8	yes	complemented
53	C₂×D₅×Dic₃	C₂×C₄	1	4	yes	—
54	C₂×D₅×Dic₃	C₂×C₄	1	4	yes	—
55	C₂×C₃×C₅×C₈	—	2	2	no	—
56	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
57	C₄×Dic₁₅	C₂×C₄	1	2	yes	—
58	C₄×Dic₁₅	C₂³	1	2	yes	—
59	C₂×C₃⋊#168	—	2	2	no	—
60	C₂×C₃⋊#168	C₂³	1	2	yes	—
61	C₄×C₅×Dic₃	C₂×C₄	1	2	yes	—
62	C₄×C₅×Dic₃	C₂³	1	2	yes	—
63	C₂×C₅×C₃⋊C₈	—	2	2	no	—
64	C₂×C₅×C₃⋊C₈	C₂³	1	2	yes	—
65	C₂×C₃×#168	—	2	2	no	—
66	C₂×C₃×#168	C₂³	1	2	yes	—
67	C₃×C₈×D₅	—	2	8	no	—
68	Dic₃×Dic₅	C₂×C₄	1	4	yes	—
69	Dic₃×Dic₅	C₂×C₄	1	4	yes	—
70	D₅×C₃⋊C₈	—	2	8	no	—
71	C₂³×C₃×C₈	—	5	1	no	—
72	C₂²×C₄×Dic₃	—	5	1	no	—
73	C₂³×C₃⋊C₈	—	5	1	no	—
74	C₂×Dic₃⋊C₈	—	5	1	no	—
75	C₂×Dic₃⋊C₈	—	5	1	no	—
76	C₂×Dic₃⋊C₈	—	5	1	no	—
77	C₂×Dic₃⋊C₈	—	5	8	no	—
78	C₂×Dic₃⋊C₈	D₅	1	1	yes	characteristic, direct product factor
79	C₂²×C₄×D₅	—	3	1	no	—
80	C₂²×C₄×D₅	—	3	1	no	—
81	C₂²×C₄×D₅	C₂×D₃	1	1	yes	characteristic
82	C₂²×C₅×C₈	—	3	1	no	—
83	C₂²×C₅×C₈	C₂×D₃	1	1	yes	characteristic
84	C₂×C₄²×C₅	—	3	1	no	—
85	C₂×C₄×Dic₅	—	3	1	no	—
86	C₂×C₄×Dic₅	—	3	1	no	—
87	C₂×C₄×Dic₅	—	3	1	no	—
88	C₂²×#168	—	3	1	no	—
89	C₂²×#168	C₂×D₃	1	1	yes	characteristic
90	C₂×C₈×D₅	—	2	4	no	—
91	C₂×C₈×D₅	—	3	4	no	—
92	C₂×C₈×D₅	—	6	4	no	—
93	C₂×C₈×D₅	C₂×D₃	1	4	yes	—
94	C₄²×D₅	—	3	4	no	—
95	C₄²×D₅	—	3	4	no	—
96	C₅×C₄⋊C₈	—	3	4	no	—
97	#3946	—	3	4	no	—
98	#3946	—	3	4	no	—
99	C₄⋊#168	—	3	4	no	—
100	C₂²×C₄⋊C₈	—	15	1	no	Sylow
101	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
102	C₂²×C₃×D₅	C₄⋊C₄	1	4	yes	—
103	C₂²×C₃×D₅	C₂×C₈	1	4	yes	—
104	C₂²×C₃×D₅	M₁₆	1	4	yes	—
105	C₂²×C₃×D₅	C₂²×C₄	1	2	yes	—
106	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
107	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
108	C₂×C₃×C₄×C₅	C₂×Q₈	1	2	yes	—
109	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
110	C₂×Dic₁₅	—	2	2	no	—
111	C₂×Dic₁₅	C₂×C₈	1	4	yes	complemented
112	C₂×Dic₁₅	C₂²×C₄	1	2	yes	—
113	C₂×Dic₁₅	C₂²×C₄	1	2	yes	—
114	C₂×C₅×Dic₃	—	2	2	no	—
115	C₂×C₅×Dic₃	C₂×C₈	1	4	yes	complemented
116	C₂×C₅×Dic₃	C₂²×C₄	1	2	yes	—
117	C₂×C₅×Dic₃	C₂²×C₄	1	2	yes	—
118	C₂×C₃×Dic₅	C₄⋊C₄	1	4	yes	—
119	C₂×C₃×Dic₅	C₂²×C₄	1	2	yes	—
120	C₃×C₄×D₅	C₄⋊C₄	1	8	yes	—
121	C₃×C₄×D₅	C₂×D₄	1	4	yes	—
122	C₃×C₄×D₅	C₂×Q₈	1	4	yes	—
123	D₅×Dic₃	—	2	8	no	—
124	D₅×Dic₃	C₂×C₈	1	16	yes	complemented
125	C₃×C₅×C₈	—	2	2	no	—
126	C₃⋊#168	—	2	2	no	—
127	C₃×#168	—	2	2	no	—
128	C₅×C₃⋊C₈	—	2	2	no	—
129	C₂³×C₃×C₄	—	5	1	no	—
130	C₂³×Dic₃	—	5	1	no	—
131	C₂³×Dic₃	—	5	1	no	—
132	C₂²×C₃×C₈	—	5	1	no	—
133	C₂²×C₃×C₈	—	5	4	no	—
134	C₂²×C₃×C₈	—	10	4	no	—
135	C₂²×C₃×C₈	C₂×D₅	1	1	yes	characteristic
136	C₂×C₄×Dic₃	—	5	1	no	—
137	C₂×C₄×Dic₃	—	5	1	no	—
138	C₂×C₄×Dic₃	—	5	1	no	—
139	C₂×C₄×Dic₃	—	5	4	no	—
140	C₂×C₄×Dic₃	—	5	4	no	—
141	C₂×C₄×Dic₃	C₂×D₅	1	1	yes	characteristic
142	C₂²×C₃⋊C₈	—	5	1	no	—
143	C₂²×C₃⋊C₈	—	5	4	no	—
144	C₂²×C₃⋊C₈	—	10	4	no	—
145	C₂²×C₃⋊C₈	C₂×D₅	1	1	yes	characteristic
146	Dic₃⋊C₈	—	5	4	no	—
147	Dic₃⋊C₈	—	5	4	no	—
148	Dic₃⋊C₈	—	5	4	no	—
149	Dic₃⋊C₈	C₂×D₅	1	4	yes	direct product factor
150	C₂³×D₅	C₄×D₃	1	1	yes	characteristic
151	C₂²×C₄×C₅	—	3	1	no	—
152	C₂²×C₄×C₅	—	3	1	no	—
153	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
154	C₂²×Dic₅	—	3	1	no	—
155	C₂²×Dic₅	—	3	1	no	—
156	C₂²×Dic₅	C₄×D₃	1	1	yes	characteristic
157	C₂×C₄×D₅	—	3	8	no	—
158	C₂×C₄×D₅	—	3	4	no	—
159	C₂×C₄×D₅	—	3	4	no	—
160	C₂×C₄×D₅	—	6	4	no	—
161	C₂×C₄×D₅	Dic₆	1	4	yes	—
162	C₂×C₄×D₅	C₄×D₃	1	2	yes	—
163	C₂×C₄×D₅	#67	1	4	yes	—
164	C₂×C₄×D₅	C₂²×D₃	1	2	yes	—
165	C₂×C₅×C₈	—	2	2	no	—
166	C₂×C₅×C₈	—	3	2	no	—
167	C₂×C₅×C₈	—	6	2	no	—
168	C₂×C₅×C₈	C₂²×D₃	1	2	yes	—
169	C₄²×C₅	—	3	2	no	—
170	C₄²×C₅	—	3	2	no	—
171	C₄×Dic₅	—	3	2	no	—
172	C₄×Dic₅	—	3	2	no	—
173	C₄×Dic₅	—	3	4	no	—
174	C₄×Dic₅	—	3	4	no	—
175	C₂×#168	—	2	2	no	—
176	C₂×#168	—	3	2	no	—
177	C₂×#168	—	6	2	no	—
178	C₂×#168	C₂²×D₃	1	2	yes	—
179	C₈×D₅	—	2	8	no	—
180	C₈×D₅	—	6	8	no	—
181	C₂³×C₈	—	5	1	no	—
182	C₂³×C₈	—	15	1	no	—
183	C₂²×C₄²	—	15	1	no	—
184	C₂×C₄⋊C₈	—	3	1	no	—
185	C₂×C₄⋊C₈	—	15	8	no	—
186	C₂×C₄⋊C₈	—	15	1	no	—
187	C₂×C₄⋊C₈	—	15	1	no	—
188	C₂×C₄⋊C₈	—	15	1	no	—
189	C₂²×C₃×C₅	C₂×C₄⋊C₄	1	2	yes	—
190	C₂²×C₃×C₅	C₂²×C₈	1	2	yes	—
191	C₂²×C₃×C₅	C₂×M₁₆	1	2	yes	—
192	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
193	C₂×C₃×D₅	C₄⋊C₈	1	16	yes	complemented
194	C₂×C₃×D₅	C₂×C₄⋊C₄	1	4	yes	—
195	C₂×C₃×D₅	C₂²×C₈	1	4	yes	—
196	C₂×C₃×D₅	C₂×M₁₆	1	4	yes	—
197	C₃×C₄×C₅	C₂×C₄⋊C₄	1	2	yes	—
198	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
199	C₃×C₄×C₅	C₂²×Q₈	1	1	yes	characteristic
200	Dic₁₅	—	2	2	no	—
201	Dic₁₅	C₂²×C₈	1	4	yes	complemented
202	C₃×Dic₅	C₂×C₄⋊C₄	1	4	yes	—
203	C₅×Dic₃	—	2	2	no	—
204	C₅×Dic₃	C₂²×C₈	1	4	yes	complemented
205	C₂⁴×C₃	—	5	1	no	—
206	C₂²×C₃×C₄	—	5	1	no	—
207	C₂²×C₃×C₄	—	5	2	no	—
208	C₂²×C₃×C₄	—	5	4	no	—
209	C₂²×C₃×C₄	—	5	4	no	—
210	C₂²×C₃×C₄	—	5	2	no	—
211	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
212	C₂²×Dic₃	—	5	1	no	—
213	C₂²×Dic₃	—	5	8	no	—
214	C₂²×Dic₃	—	5	4	no	—
215	C₂²×Dic₃	—	5	1	no	—
216	C₂²×Dic₃	—	5	4	no	—
217	C₂²×Dic₃	—	10	4	no	—
218	C₂²×Dic₃	C₄×D₅	1	1	yes	characteristic
219	C₂²×Dic₃	C₄×D₅	1	1	yes	characteristic
220	C₂×C₃×C₈	—	2	2	no	—
221	C₂×C₃×C₈	—	5	2	no	—
222	C₂×C₃×C₈	—	10	8	no	—
223	C₂×C₃×C₈	—	10	2	no	—
224	C₂×C₃×C₈	C₂²×D₅	1	2	yes	—
225	C₄×Dic₃	—	5	2	no	—
226	C₄×Dic₃	—	5	2	no	—
227	C₄×Dic₃	—	5	4	no	—
228	C₄×Dic₃	—	5	4	no	—
229	C₄×Dic₃	C₄×D₅	1	2	yes	—
230	C₄×Dic₃	C₂²×D₅	1	2	yes	—
231	C₂×C₃⋊C₈	—	2	2	no	—
232	C₂×C₃⋊C₈	—	5	2	no	—
233	C₂×C₃⋊C₈	—	10	8	no	—
234	C₂×C₃⋊C₈	—	10	2	no	—
235	C₂×C₃⋊C₈	C₂²×D₅	1	2	yes	—
236	C₂³×C₅	C₂×C₄×D₃	1	1	yes	characteristic
237	C₂²×D₅	D₃×C₈	1	4	yes	—
238	C₂²×D₅	ΓL(1,𝔽₂₅)	1	4	yes	—
239	C₂²×D₅	Dic₃⋊C₄	1	4	yes	—
240	C₂²×D₅	C₂×C₄×D₃	1	2	yes	—
241	C₂×C₄×C₅	—	3	4	no	—
242	C₂×C₄×C₅	—	3	2	no	—
243	C₂×C₄×C₅	—	3	2	no	—
244	C₂×C₄×C₅	—	6	2	no	—
245	C₂×C₄×C₅	C₂×Dic₆	1	2	yes	—
246	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
247	C₂×C₄×C₅	C₂×#67	1	2	yes	—
248	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
249	C₂×Dic₅	—	3	4	no	—
250	C₂×Dic₅	—	3	2	no	—
251	C₂×Dic₅	—	3	2	no	—
252	C₂×Dic₅	—	6	2	no	—
253	C₂×Dic₅	Dic₃⋊C₄	1	4	yes	—
254	C₂×Dic₅	C₂×C₄×D₃	1	2	yes	—
255	C₄×D₅	—	3	16	no	—
256	C₄×D₅	—	6	8	no	—
257	C₄×D₅	Dic₃⋊C₄	1	8	yes	—
258	C₄×D₅	C₂×Dic₆	1	4	yes	—
259	C₄×D₅	C₂×#67	1	4	yes	—
260	C₅×C₈	—	2	2	no	—
261	C₅×C₈	—	6	2	no	—
262	#168	—	2	2	no	—
263	#168	—	6	2	no	—
264	C₂³×C₄	—	5	1	no	—
265	C₂³×C₄	—	15	1	no	—
266	C₂³×C₄	—	15	1	no	—
267	C₂²×C₈	—	3	1	no	—
268	C₂²×C₈	—	5	1	no	—
269	C₂²×C₈	—	5	4	no	—
270	C₂²×C₈	—	10	4	no	—
271	C₂²×C₈	—	15	4	no	—
272	C₂²×C₈	—	15	1	no	—
273	C₂²×C₈	—	30	4	no	—
274	C₂²×C₈	D₃×D₅	1	1	yes	characteristic
275	C₂×C₄²	—	3	1	no	—
276	C₂×C₄²	—	15	4	no	—
277	C₂×C₄²	—	15	4	no	—
278	C₂×C₄²	—	15	1	no	—
279	C₂×C₄²	—	15	1	no	—
280	C₂×C₄²	—	15	1	no	—
281	C₄⋊C₈	—	3	4	no	—
282	C₄⋊C₈	—	15	4	no	—
283	C₄⋊C₈	—	15	4	no	—
284	C₄⋊C₈	—	15	4	no	—
285	C₂×C₃×C₅	C₂×C₄⋊C₈	1	4	yes	complemented
286	C₂×C₃×C₅	C₂²×C₄⋊C₄	1	1	yes	characteristic
287	C₂×C₃×C₅	C₂³×C₈	1	1	yes	characteristic
288	C₂×C₃×C₅	C₂²×M₁₆	1	1	yes	characteristic
289	C₃×D₅	C₂×C₄⋊C₈	1	8	yes	complemented
290	C₂³×C₃	—	5	2	no	—
291	C₂³×C₃	—	5	4	no	—
292	C₂³×C₃	—	5	4	no	—
293	C₂³×C₃	—	5	4	no	—
294	C₂³×C₃	C₂×C₄×D₅	1	1	yes	characteristic
295	C₂×C₃×C₄	—	5	2	no	—
296	C₂×C₃×C₄	—	5	4	no	—
297	C₂×C₃×C₄	—	5	4	no	—
298	C₂×C₃×C₄	—	5	4	no	—
299	C₂×C₃×C₄	—	5	8	no	—
300	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
301	C₂×C₃×C₄	D₄×D₅	1	2	yes	—
302	C₂×C₃×C₄	Q₈×D₅	1	2	yes	—
303	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
304	C₂×Dic₃	—	2	2	no	—
305	C₂×Dic₃	—	5	2	no	—
306	C₂×Dic₃	—	5	4	no	—
307	C₂×Dic₃	—	5	16	no	—
308	C₂×Dic₃	—	5	2	no	—
309	C₂×Dic₃	—	10	8	no	—
310	C₂×Dic₃	—	10	2	no	—
311	C₂×Dic₃	C₈×D₅	1	4	yes	complemented
312	C₂×Dic₃	C₂×C₄×D₅	1	2	yes	—
313	C₂×Dic₃	C₂×C₄×D₅	1	2	yes	—
314	C₃×C₈	—	2	2	no	—
315	C₃×C₈	—	10	2	no	—
316	C₃⋊C₈	—	2	2	no	—
317	C₃⋊C₈	—	10	2	no	—
318	C₂²×C₅	C₂×D₃×C₈	1	2	yes	—
319	C₂²×C₅	C₂×ΓL(1,𝔽₂₅)	1	2	yes	—
320	C₂²×C₅	C₂×Dic₃⋊C₄	1	2	yes	—
321	C₂²×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
322	C₂×D₅	Dic₃⋊C₈	1	16	yes	direct product factor
323	C₂×D₅	C₂×D₃×C₈	1	4	yes	—
324	C₂×D₅	C₂×ΓL(1,𝔽₂₅)	1	4	yes	—
325	C₂×D₅	C₂×Dic₃⋊C₄	1	4	yes	—
326	C₄×C₅	—	3	4	no	—
327	C₄×C₅	—	6	2	no	—
328	C₄×C₅	C₂×Dic₃⋊C₄	1	2	yes	—
329	C₄×C₅	C₂²×Dic₆	1	1	yes	characteristic
330	C₄×C₅	C₂²×#67	1	1	yes	characteristic
331	Dic₅	—	3	4	no	—
332	Dic₅	—	6	2	no	—
333	Dic₅	C₂×Dic₃⋊C₄	1	4	yes	—
334	C₂⁴	—	5	1	no	—
335	C₂²×C₄	—	3	1	no	—
336	C₂²×C₄	—	3	1	no	—
337	C₂²×C₄	—	5	1	no	—
338	C₂²×C₄	—	5	4	no	—
339	C₂²×C₄	—	5	2	no	—
340	C₂²×C₄	—	5	4	no	—
341	C₂²×C₄	—	5	2	no	—
342	C₂²×C₄	—	15	4	no	—
343	C₂²×C₄	—	15	8	no	—
344	C₂²×C₄	—	15	4	no	—
345	C₂²×C₄	—	15	1	no	—
346	C₂²×C₄	—	15	1	no	—
347	C₂²×C₄	—	30	4	no	—
348	C₂²×C₄	C₂×D₃×D₅	1	1	yes	characteristic
349	C₂×C₈	—	2	2	no	—
350	C₂×C₈	—	3	2	no	—
351	C₂×C₈	—	5	2	no	—
352	C₂×C₈	—	6	2	no	—
353	C₂×C₈	—	10	8	no	—
354	C₂×C₈	—	10	2	no	—
355	C₂×C₈	—	15	2	no	—
356	C₂×C₈	—	30	8	no	—
357	C₂×C₈	—	30	2	no	—
358	C₂×C₈	C₂×D₃×D₅	1	2	yes	—
359	C₄²	—	3	2	no	—
360	C₄²	—	3	2	no	—
361	C₄²	—	15	4	no	—
362	C₄²	—	15	4	no	—
363	C₄²	—	15	2	no	—
364	C₄²	—	15	2	no	—
365	C₃×C₅	C₂²×C₄⋊C₈	1	1	yes	characteristic, complemented, Hall
366	C₂²×C₃	—	5	4	no	—
367	C₂²×C₃	—	5	4	no	—
368	C₂²×C₃	—	5	4	no	—
369	C₂²×C₃	—	5	16	no	—
370	C₂²×C₃	D₅×C₄⋊C₄	1	2	yes	—
371	C₂²×C₃	C₂×C₈×D₅	1	2	yes	—
372	C₂²×C₃	D₅×M₁₆	1	2	yes	—
373	C₂²×C₃	C₂²×C₄×D₅	1	1	yes	characteristic
374	C₃×C₄	—	5	4	no	—
375	C₃×C₄	D₅×C₄⋊C₄	1	2	yes	—
376	C₃×C₄	C₂×D₄×D₅	1	1	yes	characteristic
377	C₃×C₄	C₂×Q₈×D₅	1	1	yes	characteristic
378	Dic₃	—	2	2	no	—
379	Dic₃	—	5	4	no	—
380	Dic₃	—	10	2	no	—
381	Dic₃	C₂×C₈×D₅	1	4	yes	complemented
382	C₂×C₅	C₂×Dic₃⋊C₈	1	4	yes	complemented
383	C₂×C₅	C₂²×D₃×C₈	1	1	yes	characteristic
384	C₂×C₅	C₂²×ΓL(1,𝔽₂₅)	1	1	yes	characteristic
385	C₂×C₅	C₂²×Dic₃⋊C₄	1	1	yes	characteristic
386	D₅	C₂×Dic₃⋊C₈	1	8	yes	direct product factor
387	C₂³	—	5	4	no	—
388	C₂³	—	5	2	no	—
389	C₂³	—	5	4	no	—
390	C₂³	—	5	4	no	—
391	C₂³	C₄×D₃×D₅	1	1	yes	characteristic
392	C₂×C₄	—	3	2	no	—
393	C₂×C₄	—	3	4	no	—
394	C₂×C₄	—	3	2	no	—
395	C₂×C₄	—	5	4	no	—
396	C₂×C₄	—	5	2	no	—
397	C₂×C₄	—	5	8	no	—
398	C₂×C₄	—	5	4	no	—
399	C₂×C₄	—	5	4	no	—
400	C₂×C₄	—	6	2	no	—
401	C₂×C₄	—	15	16	no	—
402	C₂×C₄	—	15	2	no	—
403	C₂×C₄	—	15	4	no	—
404	C₂×C₄	—	15	2	no	—
405	C₂×C₄	—	30	8	no	—
406	C₂×C₄	—	30	2	no	—
407	C₂×C₄	D₅×Dic₆	1	2	yes	—
408	C₂×C₄	C₄×D₃×D₅	1	1	yes	characteristic
409	C₂×C₄	D₅×#67	1	2	yes	—
410	C₂×C₄	C₂²×D₃×D₅	1	1	yes	characteristic
411	C₈	—	2	2	no	—
412	C₈	—	6	2	no	—
413	C₈	—	10	2	no	—
414	C₈	—	30	2	no	—
415	C₂×C₃	—	5	8	no	—
416	C₂×C₃	D₅×C₄⋊C₈	1	4	yes	complemented
417	C₂×C₃	C₂×D₅×C₄⋊C₄	1	1	yes	characteristic
418	C₂×C₃	C₂²×C₈×D₅	1	1	yes	characteristic
419	C₂×C₃	C₂×D₅×M₁₆	1	1	yes	characteristic
420	C₅	C₂²×Dic₃⋊C₈	1	1	yes	characteristic, complemented, Sylow
421	C₂²	—	5	4	no	—
422	C₂²	—	5	4	no	—
423	C₂²	—	5	4	no	—
424	C₂²	—	5	16	no	—
425	C₂²	D₃×C₈×D₅	1	2	yes	—
426	C₂²	D₅×ΓL(1,𝔽₂₅)	1	2	yes	—
427	C₂²	D₅×Dic₃⋊C₄	1	2	yes	—
428	C₂²	C₂×C₄×D₃×D₅	1	1	yes	characteristic
429	C₄	—	3	4	no	—
430	C₄	—	5	4	no	—
431	C₄	—	6	2	no	—
432	C₄	—	15	4	no	—
433	C₄	—	30	2	no	—
434	C₄	D₅×Dic₃⋊C₄	1	2	yes	—
435	C₄	C₂×D₅×Dic₆	1	1	yes	characteristic
436	C₄	C₂×D₅×#67	1	1	yes	characteristic
437	C₃	C₂×D₅×C₄⋊C₈	1	1	yes	characteristic, complemented, Sylow
438	C₂	—	5	8	no	—
439	C₂	D₅×Dic₃⋊C₈	1	4	yes	direct product factor
440	C₂	C₂×D₃×C₈×D₅	1	1	yes	characteristic
441	C₂	C₂×D₅×ΓL(1,𝔽₂₅)	1	1	yes	characteristic
442	C₂	C₂×D₅×Dic₃⋊C₄	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	C₂×D₃×D₅
commutator	C₂×C₃×C₅	C₂³×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
hypercenter	C₂²×C₈	D₃×D₅
hypocenter	C₃×C₅	C₂²×C₄⋊C₈
LCS	G ▷ C₂×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂²×C₄ ◁ C₂²×C₈

Complements

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

N	H ≅ G/N	type
4. C₂×#91098	C₂	semidirect
5. C₂×C₅×Dic₃⋊C₈	C₂	semidirect
6. C₂×Dic₃⋊#168	C₂	semidirect
7. C₂×#90983	C₂	semidirect
8. D₅×Dic₃⋊C₈	C₂	direct (N × H)
27. #91098	C₂²	semidirect
28. C₅×Dic₃⋊C₈	C₂²	semidirect
29. Dic₃⋊#168	C₂²	semidirect
30. #90983	C₂²	semidirect
52. C₂×D₅×Dic₃	C₈	semidirect
78. C₂×Dic₃⋊C₈	D₅	direct (N × H)
111. C₂×Dic₁₅	C₂×C₈	semidirect
115. C₂×C₅×Dic₃	C₂×C₈	semidirect
124. D₅×Dic₃	C₂×C₈	semidirect
149. Dic₃⋊C₈	C₂×D₅	direct (N × H)
193. C₂×C₃×D₅	C₄⋊C₈	semidirect
201. Dic₁₅	C₂²×C₈	semidirect
204. C₅×Dic₃	C₂²×C₈	semidirect
285. C₂×C₃×C₅	C₂×C₄⋊C₈	semidirect
289. C₃×D₅	C₂×C₄⋊C₈	semidirect
311. C₂×Dic₃	C₈×D₅	semidirect
322. C₂×D₅	Dic₃⋊C₈	direct (N × H)
365. C₃×C₅	C₂²×C₄⋊C₈	semidirect
381. Dic₃	C₂×C₈×D₅	semidirect
382. C₂×C₅	C₂×Dic₃⋊C₈	semidirect
386. D₅	C₂×Dic₃⋊C₈	direct (N × H)
416. C₂×C₃	D₅×C₄⋊C₈	semidirect
420. C₅	C₂²×Dic₃⋊C₈	semidirect
437. C₃	C₂×D₅×C₄⋊C₈	semidirect
439. C₂	D₅×Dic₃⋊C₈	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×#91098	2
C₂×C₅×Dic₃⋊C₈	2
C₂×Dic₃⋊#168	2
C₂×#90983	2
D₅×Dic₃⋊C₈	2
C₂×D₅×C₄⋊C₈	3
C₂²×Dic₃⋊C₈	5

Subgroups — C2×D5×Dic3⋊C8 #14412977

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×D₅×Dic₃⋊C₈ #14412977