Subgroups — C₂×C₅×Dic₃×D₈ #14415988

Order 1920.

1232 conjugacy classes of subgroups.

The subgroup lattice has 332 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×C₅×D₈	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅×D₄×Dic₃	C₂	1	2	yes	maximal, complemented
3	C₂×C₅×#832	C₂	1	2	yes	maximal, complemented
4	C₅×Dic₃×D₈	C₂	1	8	yes	maximal, direct product factor
5	C₂×C₅×#818	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₅×C₈×Dic₃	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₄×C₅×D₈	—	3	1	no	maximal, Hall
8	C₂²×C₃×C₅×D₄	C₂²	1	2	yes	—
9	C₂³×C₅×Dic₃	—	2	2	no	—
10	C₂×C₃×C₅×D₈	C₄	1	8	yes	complemented
11	C₂×C₃×C₅×D₈	C₂²	1	4	yes	—
12	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
13	C₂×C₅×#217	—	2	2	no	—
14	C₅×D₄×Dic₃	—	2	4	no	—
15	C₅×D₄×Dic₃	C₂²	1	8	yes	complemented
16	C₂×C₅×C₄⋊Dic₃	C₂²	1	2	yes	—
17	C₂×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic
18	C₂²×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic
19	C₅×#832	C₂²	1	8	yes	complemented
20	C₅×#818	C₂²	1	4	yes	complemented
21	C₅×C₈×Dic₃	C₂²	1	4	yes	complemented
22	C₂×Dic₃×D₈	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
23	C₂²×C₅×D₈	D₃	1	1	yes	characteristic
24	C₂×C₄×C₅×D₄	—	3	2	no	—
25	C₄×C₅×D₈	—	3	8	no	—
26	C₂×C₅×#107	—	3	1	no	—
27	C₂×C₅×#102	—	3	2	no	—
28	C₂×C₄×C₅×C₈	—	3	1	no	—
29	C₂⁴×C₃×C₅	—	2	2	no	—
30	C₂×C₃×C₅×D₄	—	2	2	no	—
31	C₂×C₃×C₅×D₄	—	2	4	no	—
32	C₂×C₃×C₅×D₄	C₂×C₄	1	8	yes	complemented
33	C₂×C₃×C₅×D₄	C₂³	1	4	yes	—
34	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
35	C₂²×C₅×Dic₃	—	2	2	no	—
36	C₂²×C₅×Dic₃	—	2	8	no	—
37	C₂²×C₅×Dic₃	—	4	8	no	—
38	C₂²×C₅×Dic₃	D₄	1	1	yes	characteristic
39	C₂²×C₅×Dic₃	D₄	1	1	yes	characteristic
40	C₃×C₅×D₈	C₂×C₄	1	16	yes	complemented
41	C₂×C₃×C₅×C₈	C₂×C₄	1	4	yes	complemented
42	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
43	C₅×#217	—	2	8	no	—
44	C₅×C₄⋊Dic₃	—	2	2	no	—
45	C₅×C₄⋊Dic₃	C₂³	1	4	yes	—
46	C₄×C₅×Dic₃	D₄	1	2	yes	—
47	C₄×C₅×Dic₃	C₂³	1	2	yes	—
48	C₂×C₅×C₃⋊C₈	—	2	2	no	—
49	C₂×C₅×C₃⋊C₈	C₂³	1	2	yes	—
50	C₂²×C₃×D₈	C₂×C₅	1	1	yes	characteristic
51	C₂×D₄×Dic₃	C₂×C₅	1	2	yes	complemented
52	C₂×#832	C₂×C₅	1	2	yes	complemented
53	Dic₃×D₈	C₂×C₅	1	8	yes	direct product factor
54	C₂×#818	C₂×C₅	1	1	yes	characteristic, complemented
55	C₂×C₈×Dic₃	C₂×C₅	1	1	yes	characteristic, complemented
56	C₂²×C₅×D₄	C₂×D₃	1	2	yes	—
57	C₂³×C₄×C₅	—	6	2	no	—
58	C₂×C₅×D₈	Dic₃	1	8	yes	direct product factor
59	C₂×C₅×D₈	C₂×D₃	1	4	yes	—
60	C₂²×C₅×C₈	—	3	1	no	—
61	C₂²×C₅×C₈	C₂×D₃	1	1	yes	characteristic
62	C₄×C₅×D₄	—	3	8	no	—
63	C₄×C₅×D₄	—	6	4	no	—
64	C₂×C₅×C₄⋊C₄	—	3	2	no	—
65	C₂×C₅×C₂²⋊C₄	—	6	2	no	—
66	C₂×C₄²×C₅	—	3	1	no	—
67	C₅×#107	—	3	4	no	—
68	C₅×#102	—	3	8	no	—
69	C₄×C₅×C₈	—	3	4	no	—
70	C₂×C₄×D₈	—	3	1	no	Sylow
71	C₂³×C₃×C₅	—	2	8	no	—
72	C₂³×C₃×C₅	—	2	4	no	—
73	C₂³×C₃×C₅	—	4	4	no	—
74	C₂³×C₃×C₅	—	4	4	no	—
75	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
76	C₃×C₅×D₄	—	2	8	no	—
77	C₃×C₅×D₄	—	2	4	no	—
78	C₃×C₅×D₄	C₂²×C₄	1	8	yes	complemented
79	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
80	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
81	C₂×C₃×C₄×C₅	#41	1	2	yes	—
82	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
83	C₂×C₅×Dic₃	—	2	2	no	—
84	C₂×C₅×Dic₃	—	2	4	no	—
85	C₂×C₅×Dic₃	—	4	4	no	—
86	C₂×C₅×Dic₃	—	4	16	no	—
87	C₂×C₅×Dic₃	D₈	1	4	yes	direct product factor
88	C₂×C₅×Dic₃	C₂×D₄	1	2	yes	—
89	C₂×C₅×Dic₃	C₂×D₄	1	2	yes	—
90	C₃×C₅×C₈	C₂²×C₄	1	4	yes	complemented
91	C₅×C₃⋊C₈	—	2	2	no	—
92	C₂²×C₃×D₄	C₂²×C₅	1	2	yes	—
93	C₂³×Dic₃	—	2	2	no	—
94	C₂×C₃×D₈	C₄×C₅	1	8	yes	complemented
95	C₂×C₃×D₈	C₂²×C₅	1	4	yes	—
96	C₂²×C₃×C₈	C₂²×C₅	1	1	yes	characteristic
97	C₂×#217	—	2	2	no	—
98	D₄×Dic₃	—	2	4	no	—
99	D₄×Dic₃	C₂²×C₅	1	8	yes	complemented
100	C₂×C₄⋊Dic₃	C₂²×C₅	1	2	yes	—
101	C₂×C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
102	C₂²×C₃⋊C₈	C₂²×C₅	1	1	yes	characteristic
103	#832	C₂²×C₅	1	8	yes	complemented
104	#818	C₂²×C₅	1	4	yes	complemented
105	C₈×Dic₃	C₂²×C₅	1	4	yes	complemented
106	C₂⁴×C₅	—	2	2	no	—
107	C₂×C₅×D₄	—	2	2	no	—
108	C₂×C₅×D₄	—	2	4	no	—
109	C₂×C₅×D₄	C₂×Dic₃	1	8	yes	complemented
110	C₂×C₅×D₄	C₂²×D₃	1	4	yes	—
111	C₂²×C₄×C₅	—	3	1	no	—
112	C₂²×C₄×C₅	—	3	1	no	—
113	C₂²×C₄×C₅	—	6	8	no	—
114	C₂²×C₄×C₅	—	6	2	no	—
115	C₂²×C₄×C₅	—	12	8	no	—
116	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
117	C₅×D₈	C₂×Dic₃	1	16	yes	direct product factor
118	C₂×C₅×C₈	—	3	2	no	—
119	C₂×C₅×C₈	—	6	2	no	—
120	C₂×C₅×C₈	C₂×Dic₃	1	4	yes	complemented
121	C₂×C₅×C₈	C₂²×D₃	1	2	yes	—
122	C₅×C₄⋊C₄	—	3	4	no	—
123	C₅×C₄⋊C₄	—	6	2	no	—
124	C₅×C₂²⋊C₄	—	6	8	no	—
125	C₄²×C₅	—	3	2	no	—
126	C₄²×C₅	—	3	2	no	—
127	C₂²×D₈	C₅×D₃	1	1	yes	characteristic
128	C₂×C₄×D₄	—	3	2	no	—
129	C₄×D₈	—	3	8	no	—
130	C₂×#107	—	3	1	no	—
131	C₂×#102	—	3	2	no	—
132	C₂×C₄×C₈	—	3	1	no	—
133	C₂²×C₃×C₅	—	2	8	no	—
134	C₂²×C₃×C₅	—	4	4	no	—
135	C₂²×C₃×C₅	—	4	4	no	—
136	C₂²×C₃×C₅	—	4	16	no	—
137	C₂²×C₃×C₅	C₄×D₄	1	2	yes	—
138	C₂²×C₃×C₅	C₂×D₈	1	2	yes	—
139	C₂²×C₃×C₅	#135	1	2	yes	—
140	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
141	C₃×C₄×C₅	C₄×D₄	1	2	yes	—
142	C₃×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
143	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
144	C₅×Dic₃	—	2	2	no	—
145	C₅×Dic₃	—	4	4	no	—
146	C₅×Dic₃	C₂×D₈	1	4	yes	direct product factor
147	C₂⁴×C₃	—	2	2	no	—
148	C₂×C₃×D₄	—	2	2	no	—
149	C₂×C₃×D₄	—	2	4	no	—
150	C₂×C₃×D₄	C₂×C₄×C₅	1	8	yes	complemented
151	C₂×C₃×D₄	C₂³×C₅	1	4	yes	—
152	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
153	C₂²×Dic₃	—	2	2	no	—
154	C₂²×Dic₃	—	2	8	no	—
155	C₂²×Dic₃	—	4	8	no	—
156	C₂²×Dic₃	C₅×D₄	1	1	yes	characteristic
157	C₂²×Dic₃	C₅×D₄	1	1	yes	characteristic
158	C₃×D₈	C₂×C₄×C₅	1	16	yes	complemented
159	C₂×C₃×C₈	C₂×C₄×C₅	1	4	yes	complemented
160	C₂×C₃×C₈	C₂³×C₅	1	2	yes	—
161	#217	—	2	8	no	—
162	C₄⋊Dic₃	—	2	2	no	—
163	C₄⋊Dic₃	C₂³×C₅	1	4	yes	—
164	C₄×Dic₃	C₅×D₄	1	2	yes	—
165	C₄×Dic₃	C₂³×C₅	1	2	yes	—
166	C₂×C₃⋊C₈	—	2	2	no	—
167	C₂×C₃⋊C₈	C₂³×C₅	1	2	yes	—
168	C₂³×C₅	—	2	8	no	—
169	C₂³×C₅	—	2	4	no	—
170	C₂³×C₅	—	4	4	no	—
171	C₂³×C₅	—	4	4	no	—
172	C₂³×C₅	D₃×D₄	1	1	yes	characteristic
173	C₅×D₄	—	2	8	no	—
174	C₅×D₄	—	2	4	no	—
175	C₅×D₄	C₂²×Dic₃	1	8	yes	complemented
176	C₂×C₄×C₅	—	3	4	no	—
177	C₂×C₄×C₅	—	3	2	no	—
178	C₂×C₄×C₅	—	3	2	no	—
179	C₂×C₄×C₅	—	6	2	no	—
180	C₂×C₄×C₅	—	6	4	no	—
181	C₂×C₄×C₅	—	12	16	no	—
182	C₂×C₄×C₅	—	12	4	no	—
183	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
184	C₂×C₄×C₅	#237	1	2	yes	—
185	C₂×C₄×C₅	C₂²×Dic₃	1	2	yes	—
186	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
187	C₅×C₈	—	6	2	no	—
188	C₅×C₈	C₂²×Dic₃	1	4	yes	complemented
189	C₂²×D₄	C₂×C₅×D₃	1	2	yes	—
190	C₂³×C₄	—	6	2	no	—
191	C₂×D₈	C₅×Dic₃	1	8	yes	direct product factor
192	C₂×D₈	C₂×C₅×D₃	1	4	yes	—
193	C₂²×C₈	—	3	1	no	—
194	C₂²×C₈	C₂×C₅×D₃	1	1	yes	characteristic
195	C₄×D₄	—	3	8	no	—
196	C₄×D₄	—	6	4	no	—
197	C₂×C₄⋊C₄	—	3	2	no	—
198	C₂×C₂²⋊C₄	—	6	2	no	—
199	C₂×C₄²	—	3	1	no	—
200	#107	—	3	4	no	—
201	#102	—	3	8	no	—
202	C₄×C₈	—	3	4	no	—
203	C₂×C₃×C₅	—	4	8	no	—
204	C₂×C₃×C₅	C₄×D₈	1	4	yes	complemented
205	C₂×C₃×C₅	C₂×C₄×D₄	1	1	yes	characteristic
206	C₂×C₃×C₅	C₂²×D₈	1	1	yes	characteristic
207	C₂×C₃×C₅	C₂×#135	1	1	yes	characteristic
208	C₂³×C₃	—	2	8	no	—
209	C₂³×C₃	—	2	4	no	—
210	C₂³×C₃	—	4	4	no	—
211	C₂³×C₃	—	4	4	no	—
212	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
213	C₃×D₄	—	2	8	no	—
214	C₃×D₄	—	2	4	no	—
215	C₃×D₄	C₂²×C₄×C₅	1	8	yes	complemented
216	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
217	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
218	C₂×C₃×C₄	C₅×#41	1	2	yes	—
219	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
220	C₂×Dic₃	—	2	2	no	—
221	C₂×Dic₃	—	2	4	no	—
222	C₂×Dic₃	—	4	4	no	—
223	C₂×Dic₃	—	4	16	no	—
224	C₂×Dic₃	C₅×D₈	1	4	yes	direct product factor
225	C₂×Dic₃	C₂×C₅×D₄	1	2	yes	—
226	C₂×Dic₃	C₂×C₅×D₄	1	2	yes	—
227	C₃×C₈	C₂²×C₄×C₅	1	4	yes	complemented
228	C₃⋊C₈	—	2	2	no	—
229	C₂²×C₅	—	2	8	no	—
230	C₂²×C₅	—	4	16	no	—
231	C₂²×C₅	—	4	4	no	—
232	C₂²×C₅	—	4	4	no	—
233	C₂²×C₅	D₃×D₈	1	2	yes	—
234	C₂²×C₅	#912	1	2	yes	—
235	C₂²×C₅	D₄×Dic₃	1	2	yes	—
236	C₂²×C₅	C₂×D₃×D₄	1	1	yes	characteristic
237	C₄×C₅	—	3	4	no	—
238	C₄×C₅	—	6	2	no	—
239	C₄×C₅	—	12	4	no	—
240	C₄×C₅	D₄×Dic₃	1	2	yes	—
241	C₄×C₅	C₂×#237	1	1	yes	characteristic
242	C₄×C₅	C₂³×Dic₃	1	1	yes	characteristic
243	C₂⁴	—	2	2	no	—
244	C₂×D₄	—	2	2	no	—
245	C₂×D₄	—	2	4	no	—
246	C₂×D₄	C₂×C₅×Dic₃	1	8	yes	complemented
247	C₂×D₄	C₂²×C₅×D₃	1	4	yes	—
248	C₂²×C₄	—	3	1	no	—
249	C₂²×C₄	—	3	1	no	—
250	C₂²×C₄	—	6	8	no	—
251	C₂²×C₄	—	6	2	no	—
252	C₂²×C₄	—	12	8	no	—
253	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
254	D₈	C₂×C₅×Dic₃	1	16	yes	direct product factor
255	C₂×C₈	—	3	2	no	—
256	C₂×C₈	—	6	2	no	—
257	C₂×C₈	C₂×C₅×Dic₃	1	4	yes	complemented
258	C₂×C₈	C₂²×C₅×D₃	1	2	yes	—
259	C₄⋊C₄	—	3	4	no	—
260	C₄⋊C₄	—	6	2	no	—
261	C₂²⋊C₄	—	6	8	no	—
262	C₄²	—	3	2	no	—
263	C₄²	—	3	2	no	—
264	C₃×C₅	C₂×C₄×D₈	1	1	yes	characteristic, complemented, Hall
265	C₂²×C₃	—	2	8	no	—
266	C₂²×C₃	—	4	16	no	—
267	C₂²×C₃	—	4	4	no	—
268	C₂²×C₃	—	4	4	no	—
269	C₂²×C₃	C₄×C₅×D₄	1	2	yes	—
270	C₂²×C₃	C₂×C₅×D₈	1	2	yes	—
271	C₂²×C₃	C₅×#135	1	2	yes	—
272	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
273	C₃×C₄	C₄×C₅×D₄	1	2	yes	—
274	C₃×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
275	C₃×C₄	C₂×C₅×#41	1	1	yes	characteristic
276	Dic₃	—	2	2	no	—
277	Dic₃	—	4	4	no	—
278	Dic₃	C₂×C₅×D₈	1	4	yes	direct product factor
279	C₂×C₅	—	4	8	no	—
280	C₂×C₅	Dic₃×D₈	1	4	yes	direct product factor
281	C₂×C₅	C₂×D₃×D₈	1	1	yes	characteristic
282	C₂×C₅	C₂×#912	1	1	yes	characteristic
283	C₂×C₅	C₂×D₄×Dic₃	1	1	yes	characteristic
284	C₂³	—	2	8	no	—
285	C₂³	—	2	4	no	—
286	C₂³	—	4	4	no	—
287	C₂³	—	4	4	no	—
288	C₂³	C₅×D₃×D₄	1	1	yes	characteristic
289	D₄	—	2	8	no	—
290	D₄	—	2	4	no	—
291	D₄	C₂²×C₅×Dic₃	1	8	yes	complemented
292	C₂×C₄	—	3	4	no	—
293	C₂×C₄	—	3	2	no	—
294	C₂×C₄	—	3	2	no	—
295	C₂×C₄	—	6	2	no	—
296	C₂×C₄	—	6	4	no	—
297	C₂×C₄	—	12	16	no	—
298	C₂×C₄	—	12	4	no	—
299	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
300	C₂×C₄	C₅×#237	1	2	yes	—
301	C₂×C₄	C₂²×C₅×Dic₃	1	2	yes	—
302	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
303	C₈	—	6	2	no	—
304	C₈	C₂²×C₅×Dic₃	1	4	yes	complemented
305	C₂×C₃	—	4	8	no	—
306	C₂×C₃	C₄×C₅×D₈	1	4	yes	complemented
307	C₂×C₃	C₂×C₄×C₅×D₄	1	1	yes	characteristic
308	C₂×C₃	C₂²×C₅×D₈	1	1	yes	characteristic
309	C₂×C₃	C₂×C₅×#135	1	1	yes	characteristic
310	C₅	C₂×Dic₃×D₈	1	1	yes	characteristic, direct product factor, Sylow
311	C₂²	—	2	8	no	—
312	C₂²	—	4	4	no	—
313	C₂²	—	4	4	no	—
314	C₂²	—	4	16	no	—
315	C₂²	C₅×D₃×D₈	1	2	yes	—
316	C₂²	C₅×#912	1	2	yes	—
317	C₂²	C₅×D₄×Dic₃	1	2	yes	—
318	C₂²	C₂×C₅×D₃×D₄	1	1	yes	characteristic
319	C₄	—	3	4	no	—
320	C₄	—	6	2	no	—
321	C₄	—	12	4	no	—
322	C₄	C₅×D₄×Dic₃	1	2	yes	—
323	C₄	C₂×C₅×#237	1	1	yes	characteristic
324	C₄	C₂³×C₅×Dic₃	1	1	yes	characteristic
325	C₃	C₂×C₄×C₅×D₈	1	1	yes	characteristic, complemented, Sylow
326	C₂	—	4	8	no	—
327	C₂	C₅×Dic₃×D₈	1	4	yes	direct product factor
328	C₂	C₂×C₅×D₃×D₈	1	1	yes	characteristic
329	C₂	C₂×C₅×#912	1	1	yes	characteristic
330	C₂	C₂×C₅×D₄×Dic₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₅	D₃×D₄
commutator	C₃×C₄	C₂³×C₄×C₅
Frattini	C₂×C₄	C₂³×C₅×D₃
Fitting, prime radical	C₂²×C₃×C₅×D₈	C₂
socle	C₂³×C₃×C₅	C₂×D₄
cosocle	C₂×C₃×C₄	C₂⁴×C₅
hypercenter	C₂²×C₅×D₈	D₃
hypocenter	C₃	C₂×C₄×C₅×D₈
LCS	G ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂³×C₅ ◁ C₂²×C₄×C₅ ◁ C₂²×C₅×D₈

Complements

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

N	H ≅ G/N	type
2. C₂×C₅×D₄×Dic₃	C₂	semidirect
3. C₂×C₅×#832	C₂	semidirect
4. C₅×Dic₃×D₈	C₂	direct (N × H)
5. C₂×C₅×#818	C₂	semidirect
6. C₂×C₅×C₈×Dic₃	C₂	semidirect
10. C₂×C₃×C₅×D₈	C₄	semidirect
15. C₅×D₄×Dic₃	C₂²	semidirect
19. C₅×#832	C₂²	semidirect
20. C₅×#818	C₂²	semidirect
21. C₅×C₈×Dic₃	C₂²	semidirect
22. C₂×Dic₃×D₈	C₅	direct (N × H)
32. C₂×C₃×C₅×D₄	C₂×C₄	semidirect
40. C₃×C₅×D₈	C₂×C₄	semidirect
41. C₂×C₃×C₅×C₈	C₂×C₄	semidirect
51. C₂×D₄×Dic₃	C₂×C₅	semidirect
52. C₂×#832	C₂×C₅	semidirect
53. Dic₃×D₈	C₂×C₅	direct (N × H)
54. C₂×#818	C₂×C₅	semidirect
55. C₂×C₈×Dic₃	C₂×C₅	semidirect
58. C₂×C₅×D₈	Dic₃	direct (N × H)
78. C₃×C₅×D₄	C₂²×C₄	semidirect
87. C₂×C₅×Dic₃	D₈	direct (N × H)
90. C₃×C₅×C₈	C₂²×C₄	semidirect
94. C₂×C₃×D₈	C₄×C₅	semidirect
99. D₄×Dic₃	C₂²×C₅	semidirect
103. #832	C₂²×C₅	semidirect
104. #818	C₂²×C₅	semidirect
105. C₈×Dic₃	C₂²×C₅	semidirect
109. C₂×C₅×D₄	C₂×Dic₃	semidirect
117. C₅×D₈	C₂×Dic₃	direct (N × H)
120. C₂×C₅×C₈	C₂×Dic₃	semidirect
146. C₅×Dic₃	C₂×D₈	direct (N × H)
150. C₂×C₃×D₄	C₂×C₄×C₅	semidirect
158. C₃×D₈	C₂×C₄×C₅	semidirect
159. C₂×C₃×C₈	C₂×C₄×C₅	semidirect
175. C₅×D₄	C₂²×Dic₃	semidirect
188. C₅×C₈	C₂²×Dic₃	semidirect
191. C₂×D₈	C₅×Dic₃	direct (N × H)
204. C₂×C₃×C₅	C₄×D₈	semidirect
215. C₃×D₄	C₂²×C₄×C₅	semidirect
224. C₂×Dic₃	C₅×D₈	direct (N × H)
227. C₃×C₈	C₂²×C₄×C₅	semidirect
246. C₂×D₄	C₂×C₅×Dic₃	semidirect
254. D₈	C₂×C₅×Dic₃	direct (N × H)
257. C₂×C₈	C₂×C₅×Dic₃	semidirect
264. C₃×C₅	C₂×C₄×D₈	semidirect
278. Dic₃	C₂×C₅×D₈	direct (N × H)
280. C₂×C₅	Dic₃×D₈	direct (N × H)
291. D₄	C₂²×C₅×Dic₃	semidirect
304. C₈	C₂²×C₅×Dic₃	semidirect
306. C₂×C₃	C₄×C₅×D₈	semidirect
310. C₅	C₂×Dic₃×D₈	direct (N × H)
325. C₃	C₂×C₄×C₅×D₈	semidirect
327. C₂	C₅×Dic₃×D₈	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×C₅×D₈	2
C₂×C₅×D₄×Dic₃	2
C₂×C₅×#832	2
C₅×Dic₃×D₈	2
C₂×C₅×#818	2
C₂×C₅×C₈×Dic₃	2
C₂×C₄×C₅×D₈	3
C₂×Dic₃×D₈	5

Subgroups — C2×C5×Dic3×D8 #14415988

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×Dic₃×D₈ #14415988