Subgroups — C₂×C₃×D₅×SD₃₂ #14478214

Order 1920.

800 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×D₅×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃×D₅×D₈	C₂	1	1	yes	maximal, characteristic
3	C₂×C₃×C₅×SD₃₂	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₃×#3960	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₃×#3959	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×D₅×SD₃₂	C₂	1	8	yes	maximal, direct product factor
7	C₂×C₃×#3932	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₃×D₅×C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×D₅×SD₃₂	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₂×C₃×Q₈×D₅	—	2	1	no	—
11	C₂×C₃×D₄×D₅	—	2	1	no	—
12	C₂×C₃×C₅×Q₁₆	C₂²	1	1	yes	characteristic, complemented
13	C₂×C₃×C₅×D₈	C₂²	1	1	yes	characteristic
14	C₂×C₃×#689	—	2	1	no	—
15	C₂×C₃×#686	—	2	1	no	—
16	C₃×D₅×Q₁₆	—	2	2	no	—
17	C₃×D₅×Q₁₆	C₂²	1	4	yes	complemented
18	C₃×D₅×D₈	—	2	2	no	—
19	C₃×D₅×D₈	C₂²	1	4	yes	—
20	C₂×C₃×Dic₂₀	C₂²	1	1	yes	characteristic, complemented
21	C₂×C₃×D₄₀	C₂²	1	1	yes	characteristic
22	C₂×C₃×C₈×D₅	C₂²	1	1	yes	characteristic
23	C₃×C₅×SD₃₂	C₂²	1	4	yes	complemented
24	C₂×C₃×C₅×C₁₆	C₂²	1	1	yes	characteristic, complemented
25	C₃×#3960	C₂²	1	4	yes	complemented
26	C₃×#3959	C₂²	1	4	yes	complemented
27	C₂×C₃×#672	C₂²	1	1	yes	characteristic, complemented
28	C₃×#3932	C₂²	1	4	yes	complemented
29	C₃×D₅×C₁₆	C₂²	1	4	yes	complemented
30	C₂²×C₃×SD₃₂	—	5	1	no	maximal, Hall
31	C₂×D₅×Q₁₆	C₂×C₃	1	1	yes	characteristic, complemented
32	C₂×D₅×D₈	C₂×C₃	1	1	yes	characteristic
33	C₂×C₅×SD₃₂	C₂×C₃	1	1	yes	characteristic, complemented
34	C₂×#3960	C₂×C₃	1	1	yes	characteristic, complemented
35	C₂×#3959	C₂×C₃	1	1	yes	characteristic, complemented
36	D₅×SD₃₂	C₂×C₃	1	8	yes	direct product factor
37	C₂×#3932	C₂×C₃	1	1	yes	characteristic, complemented
38	C₂×D₅×C₁₆	C₂×C₃	1	1	yes	characteristic, complemented
39	C₂³×C₃×D₅	—	4	1	no	—
40	C₂×C₃×C₅×Q₈	—	2	1	no	—
41	C₂×C₃×C₅×D₄	—	2	1	no	—
42	C₂×C₃×C₂²⋊D₅	—	4	1	no	—
43	C₃×Q₈×D₅	—	2	4	no	—
44	C₃×Q₈×D₅	—	4	2	no	—
45	C₃×D₄×D₅	—	2	4	no	—
46	C₃×D₄×D₅	—	4	2	no	—
47	C₂×C₃×D₂₀	—	2	1	no	—
48	C₂×C₃×C₄×D₅	—	4	1	no	—
49	C₂×C₃×C₄×D₅	D₄	1	1	yes	characteristic
50	C₂×C₃×Dic₁₀	—	2	1	no	—
51	C₂×C₃×Dic₁₀	—	4	1	no	—
52	C₃×C₅×Q₁₆	—	2	1	no	—
53	C₃×C₅×Q₁₆	C₂³	1	2	yes	complemented
54	C₃×C₅×D₈	—	2	1	no	—
55	C₃×C₅×D₈	C₂³	1	2	yes	—
56	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
57	C₃×#689	—	2	4	no	—
58	C₃×#686	—	2	4	no	—
59	C₂×C₃×#168	D₄	1	1	yes	characteristic
60	C₃×Dic₂₀	—	2	1	no	—
61	C₃×Dic₂₀	C₂³	1	2	yes	complemented
62	C₃×D₄₀	—	2	1	no	—
63	C₃×D₄₀	C₂³	1	2	yes	—
64	C₃×C₈×D₅	D₄	1	2	yes	—
65	C₃×C₈×D₅	C₂³	1	2	yes	—
66	C₃×C₅×C₁₆	C₂³	1	2	yes	complemented
67	C₃×#672	C₂³	1	2	yes	complemented
68	C₂²×C₃×Q₁₆	—	5	1	no	—
69	C₂²×C₃×D₈	—	5	1	no	—
70	C₂×C₃×SD₃₂	—	5	1	no	—
71	C₂×C₃×SD₃₂	—	5	1	no	—
72	C₂×C₃×SD₃₂	—	5	8	no	—
73	C₂×C₃×SD₃₂	—	5	1	no	—
74	C₂×C₃×SD₃₂	D₅	1	1	yes	characteristic, direct product factor
75	C₂²×C₃×C₁₆	—	5	1	no	—
76	C₂×Q₈×D₅	—	2	1	no	—
77	C₂×D₄×D₅	—	2	1	no	—
78	C₂×C₅×Q₁₆	C₂²×C₃	1	1	yes	characteristic, complemented
79	C₂×C₅×D₈	C₂²×C₃	1	1	yes	characteristic
80	C₂×#689	—	2	1	no	—
81	C₂×#686	—	2	1	no	—
82	D₅×Q₁₆	—	2	2	no	—
83	D₅×Q₁₆	C₂²×C₃	1	4	yes	complemented
84	D₅×D₈	—	2	2	no	—
85	D₅×D₈	C₂²×C₃	1	4	yes	—
86	C₂×Dic₂₀	C₂²×C₃	1	1	yes	characteristic, complemented
87	C₂×D₄₀	C₂²×C₃	1	1	yes	characteristic
88	C₂×C₈×D₅	C₂²×C₃	1	1	yes	characteristic
89	C₅×SD₃₂	C₂²×C₃	1	4	yes	complemented
90	C₂×C₅×C₁₆	C₂²×C₃	1	1	yes	characteristic, complemented
91	#3960	C₂²×C₃	1	4	yes	complemented
92	#3959	C₂²×C₃	1	4	yes	complemented
93	C₂×#672	C₂²×C₃	1	1	yes	characteristic, complemented
94	#3932	C₂²×C₃	1	4	yes	complemented
95	D₅×C₁₆	C₂²×C₃	1	4	yes	complemented
96	C₂²×SD₃₂	—	5	1	no	Sylow
97	C₂³×C₃×C₅	—	4	1	no	—
98	C₂²×C₃×D₅	—	4	1	no	—
99	C₂²×C₃×D₅	—	4	4	no	—
100	C₂²×C₃×D₅	—	8	4	no	—
101	C₂²×C₃×D₅	D₈	1	1	yes	characteristic
102	C₃×C₅×Q₈	—	2	2	no	—
103	C₃×C₅×Q₈	—	4	1	no	—
104	C₃×C₅×D₄	—	2	2	no	—
105	C₃×C₅×D₄	—	4	1	no	—
106	C₂×C₃×C₄×C₅	—	4	1	no	—
107	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
108	C₃×C₂²⋊D₅	—	4	4	no	—
109	C₂×C₃×Dic₅	—	4	1	no	—
110	C₂×C₃×Dic₅	D₈	1	1	yes	characteristic
111	C₃×D₂₀	—	2	2	no	—
112	C₃×D₂₀	—	4	1	no	—
113	C₃×C₄×D₅	—	4	4	no	—
114	C₃×C₄×D₅	D₈	1	2	yes	—
115	C₃×C₄×D₅	C₂×D₄	1	2	yes	—
116	C₃×Dic₁₀	—	2	2	no	—
117	C₃×Dic₁₀	—	4	1	no	—
118	C₃×Dic₁₀	—	4	4	no	—
119	C₃×C₅×C₈	C₂×D₄	1	1	yes	characteristic
120	C₃×C₅×C₈	C₂⁴	1	1	yes	characteristic
121	C₃×#168	C₂×D₄	1	2	yes	—
122	C₂²×C₃×Q₈	—	10	1	no	—
123	C₂²×C₃×D₄	—	10	1	no	—
124	C₂×C₃×Q₁₆	—	5	4	no	—
125	C₂×C₃×Q₁₆	—	5	1	no	—
126	C₂×C₃×Q₁₆	—	10	2	no	—
127	C₂×C₃×Q₁₆	—	10	1	no	—
128	C₂×C₃×Q₁₆	C₂×D₅	1	1	yes	characteristic, complemented
129	C₂×C₃×D₈	—	5	4	no	—
130	C₂×C₃×D₈	—	5	1	no	—
131	C₂×C₃×D₈	—	10	2	no	—
132	C₂×C₃×D₈	—	10	1	no	—
133	C₂×C₃×D₈	C₂×D₅	1	1	yes	characteristic
134	C₂²×C₃×C₈	—	5	1	no	—
135	C₃×SD₃₂	—	5	4	no	—
136	C₃×SD₃₂	—	5	4	no	—
137	C₃×SD₃₂	—	5	4	no	—
138	C₃×SD₃₂	C₂×D₅	1	4	yes	direct product factor
139	C₂×C₃×C₁₆	—	5	1	no	—
140	C₂×C₃×C₁₆	—	5	4	no	—
141	C₂×C₃×C₁₆	C₂×D₅	1	1	yes	characteristic, complemented
142	C₂³×D₅	—	4	1	no	—
143	C₂×C₅×Q₈	—	2	1	no	—
144	C₂×C₅×D₄	—	2	1	no	—
145	C₂×C₂²⋊D₅	—	4	1	no	—
146	Q₈×D₅	—	2	4	no	—
147	Q₈×D₅	—	4	2	no	—
148	D₄×D₅	—	2	4	no	—
149	D₄×D₅	—	4	2	no	—
150	C₂×D₂₀	—	2	1	no	—
151	C₂×C₄×D₅	—	4	1	no	—
152	C₂×C₄×D₅	C₃×D₄	1	1	yes	characteristic
153	C₂×Dic₁₀	—	2	1	no	—
154	C₂×Dic₁₀	—	4	1	no	—
155	C₅×Q₁₆	—	2	1	no	—
156	C₅×Q₁₆	C₂³×C₃	1	2	yes	complemented
157	C₅×D₈	—	2	1	no	—
158	C₅×D₈	C₂³×C₃	1	2	yes	—
159	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
160	#689	—	2	4	no	—
161	#686	—	2	4	no	—
162	C₂×#168	C₃×D₄	1	1	yes	characteristic
163	Dic₂₀	—	2	1	no	—
164	Dic₂₀	C₂³×C₃	1	2	yes	complemented
165	D₄₀	—	2	1	no	—
166	D₄₀	C₂³×C₃	1	2	yes	—
167	C₈×D₅	C₃×D₄	1	2	yes	—
168	C₈×D₅	C₂³×C₃	1	2	yes	—
169	C₅×C₁₆	C₂³×C₃	1	2	yes	complemented
170	#672	C₂³×C₃	1	2	yes	complemented
171	C₂²×Q₁₆	—	5	1	no	—
172	C₂²×D₈	—	5	1	no	—
173	C₂×SD₃₂	—	5	1	no	—
174	C₂×SD₃₂	—	5	1	no	—
175	C₂×SD₃₂	—	5	8	no	—
176	C₂×SD₃₂	—	5	1	no	—
177	C₂×SD₃₂	C₃×D₅	1	1	yes	characteristic, direct product factor
178	C₂²×C₁₆	—	5	1	no	—
179	C₂²×C₃×C₅	—	4	2	no	—
180	C₂²×C₃×C₅	—	8	2	no	—
181	C₂²×C₃×C₅	C₂×D₈	1	1	yes	characteristic
182	C₂×C₃×D₅	—	4	2	no	—
183	C₂×C₃×D₅	—	8	2	no	—
184	C₂×C₃×D₅	—	8	8	no	—
185	C₂×C₃×D₅	SD₃₂	1	4	yes	direct product factor
186	C₂×C₃×D₅	C₂×D₈	1	2	yes	—
187	C₃×C₄×C₅	—	4	2	no	—
188	C₃×C₄×C₅	C₂×D₈	1	1	yes	characteristic
189	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
190	C₃×Dic₅	—	4	2	no	—
191	C₃×Dic₅	C₂×D₈	1	2	yes	—
192	C₂⁴×C₃	—	20	1	no	—
193	C₂×C₃×Q₈	—	2	1	no	—
194	C₂×C₃×Q₈	—	10	4	no	—
195	C₂×C₃×Q₈	—	10	1	no	—
196	C₂×C₃×Q₈	—	20	1	no	—
197	C₂×C₃×Q₈	—	20	2	no	—
198	C₂×C₃×D₄	—	2	1	no	—
199	C₂×C₃×D₄	—	10	4	no	—
200	C₂×C₃×D₄	—	10	1	no	—
201	C₂×C₃×D₄	—	20	2	no	—
202	C₂×C₃×D₄	—	20	1	no	—
203	C₂²×C₃×C₄	—	5	1	no	—
204	C₂²×C₃×C₄	—	20	1	no	—
205	C₃×Q₁₆	—	2	1	no	—
206	C₃×Q₁₆	—	5	2	no	—
207	C₃×Q₁₆	—	10	4	no	—
208	C₃×Q₁₆	—	10	1	no	—
209	C₃×Q₁₆	C₂²×D₅	1	2	yes	complemented
210	C₃×D₈	—	2	1	no	—
211	C₃×D₈	—	5	2	no	—
212	C₃×D₈	—	10	4	no	—
213	C₃×D₈	—	10	1	no	—
214	C₃×D₈	C₂²×D₅	1	2	yes	—
215	C₂×C₃×C₈	—	5	1	no	—
216	C₂×C₃×C₈	—	5	2	no	—
217	C₂×C₃×C₈	—	5	2	no	—
218	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
219	C₃×C₁₆	—	5	2	no	—
220	C₃×C₁₆	C₂²×D₅	1	2	yes	complemented
221	C₂³×C₅	—	4	1	no	—
222	C₂²×D₅	—	4	1	no	—
223	C₂²×D₅	—	4	4	no	—
224	C₂²×D₅	—	8	4	no	—
225	C₂²×D₅	C₃×D₈	1	1	yes	characteristic
226	C₅×Q₈	—	2	2	no	—
227	C₅×Q₈	—	4	1	no	—
228	C₅×D₄	—	2	2	no	—
229	C₅×D₄	—	4	1	no	—
230	C₂×C₄×C₅	—	4	1	no	—
231	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
232	C₂²⋊D₅	—	4	4	no	—
233	C₂×Dic₅	—	4	1	no	—
234	C₂×Dic₅	C₃×D₈	1	1	yes	characteristic
235	D₂₀	—	2	2	no	—
236	D₂₀	—	4	1	no	—
237	C₄×D₅	—	4	4	no	—
238	C₄×D₅	C₃×D₈	1	2	yes	—
239	C₄×D₅	C₂×C₃×D₄	1	2	yes	—
240	Dic₁₀	—	2	2	no	—
241	Dic₁₀	—	4	1	no	—
242	Dic₁₀	—	4	4	no	—
243	C₅×C₈	C₂×C₃×D₄	1	1	yes	characteristic
244	C₅×C₈	C₂⁴×C₃	1	1	yes	characteristic
245	#168	C₂×C₃×D₄	1	2	yes	—
246	C₂²×Q₈	—	10	1	no	—
247	C₂²×D₄	—	10	1	no	—
248	C₂×Q₁₆	—	5	4	no	—
249	C₂×Q₁₆	—	5	1	no	—
250	C₂×Q₁₆	—	10	2	no	—
251	C₂×Q₁₆	—	10	1	no	—
252	C₂×Q₁₆	C₂×C₃×D₅	1	1	yes	characteristic, complemented
253	C₂×D₈	—	5	4	no	—
254	C₂×D₈	—	5	1	no	—
255	C₂×D₈	—	10	2	no	—
256	C₂×D₈	—	10	1	no	—
257	C₂×D₈	C₂×C₃×D₅	1	1	yes	characteristic
258	C₂²×C₈	—	5	1	no	—
259	SD₃₂	—	5	4	no	—
260	SD₃₂	—	5	4	no	—
261	SD₃₂	—	5	4	no	—
262	SD₃₂	C₂×C₃×D₅	1	4	yes	direct product factor
263	C₂×C₁₆	—	5	1	no	—
264	C₂×C₁₆	—	5	4	no	—
265	C₂×C₁₆	C₂×C₃×D₅	1	1	yes	characteristic, complemented
266	C₂×C₃×C₅	—	8	2	no	—
267	C₂×C₃×C₅	C₂×SD₃₂	1	2	yes	complemented
268	C₂×C₃×C₅	C₂²×D₈	1	1	yes	characteristic
269	C₃×D₅	—	8	2	no	—
270	C₃×D₅	C₂×SD₃₂	1	4	yes	direct product factor
271	C₂³×C₃	—	4	1	no	—
272	C₂³×C₃	—	5	1	no	—
273	C₂³×C₃	—	20	4	no	—
274	C₂³×C₃	—	20	1	no	—
275	C₂³×C₃	—	40	4	no	—
276	C₃×Q₈	—	2	2	no	—
277	C₃×Q₈	—	4	1	no	—
278	C₃×Q₈	—	10	2	no	—
279	C₃×Q₈	—	20	4	no	—
280	C₃×Q₈	—	20	1	no	—
281	C₃×D₄	—	2	2	no	—
282	C₃×D₄	—	4	1	no	—
283	C₃×D₄	—	10	2	no	—
284	C₃×D₄	—	20	4	no	—
285	C₃×D₄	—	20	1	no	—
286	C₂×C₃×C₄	—	4	1	no	—
287	C₂×C₃×C₄	—	5	1	no	—
288	C₂×C₃×C₄	—	5	2	no	—
289	C₂×C₃×C₄	—	5	2	no	—
290	C₂×C₃×C₄	—	20	4	no	—
291	C₂×C₃×C₄	—	20	1	no	—
292	C₂×C₃×C₄	D₄×D₅	1	1	yes	characteristic
293	C₃×C₈	—	5	2	no	—
294	C₃×C₈	D₄×D₅	1	1	yes	characteristic
295	C₃×C₈	C₂³×D₅	1	1	yes	characteristic
296	C₂²×C₅	—	4	2	no	—
297	C₂²×C₅	—	8	2	no	—
298	C₂²×C₅	C₂×C₃×D₈	1	1	yes	characteristic
299	C₂×D₅	—	4	2	no	—
300	C₂×D₅	—	8	2	no	—
301	C₂×D₅	—	8	8	no	—
302	C₂×D₅	C₃×SD₃₂	1	4	yes	direct product factor
303	C₂×D₅	C₂×C₃×D₈	1	2	yes	—
304	C₄×C₅	—	4	2	no	—
305	C₄×C₅	C₂×C₃×D₈	1	1	yes	characteristic
306	C₄×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
307	Dic₅	—	4	2	no	—
308	Dic₅	C₂×C₃×D₈	1	2	yes	—
309	C₂⁴	—	20	1	no	—
310	C₂×Q₈	—	2	1	no	—
311	C₂×Q₈	—	10	4	no	—
312	C₂×Q₈	—	10	1	no	—
313	C₂×Q₈	—	20	1	no	—
314	C₂×Q₈	—	20	2	no	—
315	C₂×D₄	—	2	1	no	—
316	C₂×D₄	—	10	4	no	—
317	C₂×D₄	—	10	1	no	—
318	C₂×D₄	—	20	2	no	—
319	C₂×D₄	—	20	1	no	—
320	C₂²×C₄	—	5	1	no	—
321	C₂²×C₄	—	20	1	no	—
322	Q₁₆	—	2	1	no	—
323	Q₁₆	—	5	2	no	—
324	Q₁₆	—	10	4	no	—
325	Q₁₆	—	10	1	no	—
326	Q₁₆	C₂²×C₃×D₅	1	2	yes	complemented
327	D₈	—	2	1	no	—
328	D₈	—	5	2	no	—
329	D₈	—	10	4	no	—
330	D₈	—	10	1	no	—
331	D₈	C₂²×C₃×D₅	1	2	yes	—
332	C₂×C₈	—	5	1	no	—
333	C₂×C₈	—	5	2	no	—
334	C₂×C₈	—	5	2	no	—
335	C₂×C₈	C₂²×C₃×D₅	1	1	yes	characteristic
336	C₁₆	—	5	2	no	—
337	C₁₆	C₂²×C₃×D₅	1	2	yes	complemented
338	C₃×C₅	C₂²×SD₃₂	1	1	yes	characteristic, complemented, Hall
339	C₂²×C₃	—	4	2	no	—
340	C₂²×C₃	—	5	2	no	—
341	C₂²×C₃	—	5	4	no	—
342	C₂²×C₃	—	8	2	no	—
343	C₂²×C₃	—	20	2	no	—
344	C₂²×C₃	—	40	8	no	—
345	C₂²×C₃	—	40	2	no	—
346	C₂²×C₃	D₅×D₈	1	1	yes	characteristic
347	C₃×C₄	—	4	2	no	—
348	C₃×C₄	—	5	2	no	—
349	C₃×C₄	—	20	2	no	—
350	C₃×C₄	D₅×D₈	1	1	yes	characteristic
351	C₃×C₄	C₂×D₄×D₅	1	1	yes	characteristic
352	C₂×C₅	—	8	2	no	—
353	C₂×C₅	C₂×C₃×SD₃₂	1	2	yes	complemented
354	C₂×C₅	C₂²×C₃×D₈	1	1	yes	characteristic
355	D₅	—	8	2	no	—
356	D₅	C₂×C₃×SD₃₂	1	4	yes	direct product factor
357	C₂³	—	4	1	no	—
358	C₂³	—	5	1	no	—
359	C₂³	—	20	4	no	—
360	C₂³	—	20	1	no	—
361	C₂³	—	40	4	no	—
362	Q₈	—	2	2	no	—
363	Q₈	—	4	1	no	—
364	Q₈	—	10	2	no	—
365	Q₈	—	20	4	no	—
366	Q₈	—	20	1	no	—
367	D₄	—	2	2	no	—
368	D₄	—	4	1	no	—
369	D₄	—	10	2	no	—
370	D₄	—	20	4	no	—
371	D₄	—	20	1	no	—
372	C₂×C₄	—	4	1	no	—
373	C₂×C₄	—	5	1	no	—
374	C₂×C₄	—	5	2	no	—
375	C₂×C₄	—	5	2	no	—
376	C₂×C₄	—	20	4	no	—
377	C₂×C₄	—	20	1	no	—
378	C₂×C₄	C₃×D₄×D₅	1	1	yes	characteristic
379	C₈	—	5	2	no	—
380	C₈	C₃×D₄×D₅	1	1	yes	characteristic
381	C₈	C₂³×C₃×D₅	1	1	yes	characteristic
382	C₂×C₃	—	5	4	no	—
383	C₂×C₃	—	8	2	no	—
384	C₂×C₃	—	40	2	no	—
385	C₂×C₃	D₅×SD₃₂	1	2	yes	direct product factor
386	C₂×C₃	C₂×D₅×D₈	1	1	yes	characteristic
387	C₅	C₂²×C₃×SD₃₂	1	1	yes	characteristic, complemented, Sylow
388	C₂²	—	4	2	no	—
389	C₂²	—	5	4	no	—
390	C₂²	—	5	2	no	—
391	C₂²	—	8	2	no	—
392	C₂²	—	20	2	no	—
393	C₂²	—	40	8	no	—
394	C₂²	—	40	2	no	—
395	C₂²	C₃×D₅×D₈	1	1	yes	characteristic
396	C₄	—	4	2	no	—
397	C₄	—	5	2	no	—
398	C₄	—	20	2	no	—
399	C₄	C₃×D₅×D₈	1	1	yes	characteristic
400	C₄	C₂×C₃×D₄×D₅	1	1	yes	characteristic
401	C₃	C₂×D₅×SD₃₂	1	1	yes	characteristic, direct product factor, Sylow
402	C₂	—	5	4	no	—
403	C₂	—	8	2	no	—
404	C₂	—	40	2	no	—
405	C₂	C₃×D₅×SD₃₂	1	2	yes	direct product factor
406	C₂	C₂×C₃×D₅×D₈	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃	D₅×D₈
commutator, cosocle	C₅×C₈	C₂⁴×C₃
Frattini	C₈	C₂³×C₃×D₅
Fitting	C₂×C₃×C₅×SD₃₂	C₂
socle	C₂²×C₃×C₅	C₂×D₈
prime radical	C₂×C₃×D₅×D₈	C₂
hypercenter	C₂×C₃×SD₃₂	D₅
hypocenter	C₅	C₂²×C₃×SD₃₂
LCS	G ▷ C₅×C₈ ▷ C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₃ ◁ C₂×C₃×C₄ ◁ C₂×C₃×C₈ ◁ C₂×C₃×SD₃₂

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×D₅×Q₁₆	C₂	semidirect
3. C₂×C₃×C₅×SD₃₂	C₂	semidirect
4. C₂×C₃×#3960	C₂	semidirect
5. C₂×C₃×#3959	C₂	semidirect
6. C₃×D₅×SD₃₂	C₂	direct (N × H)
7. C₂×C₃×#3932	C₂	semidirect
8. C₂×C₃×D₅×C₁₆	C₂	semidirect
9. C₂×D₅×SD₃₂	C₃	direct (N × H)
12. C₂×C₃×C₅×Q₁₆	C₂²	semidirect
17. C₃×D₅×Q₁₆	C₂²	semidirect
20. C₂×C₃×Dic₂₀	C₂²	semidirect
23. C₃×C₅×SD₃₂	C₂²	semidirect
24. C₂×C₃×C₅×C₁₆	C₂²	semidirect
25. C₃×#3960	C₂²	semidirect
26. C₃×#3959	C₂²	semidirect
27. C₂×C₃×#672	C₂²	semidirect
28. C₃×#3932	C₂²	semidirect
29. C₃×D₅×C₁₆	C₂²	semidirect
31. C₂×D₅×Q₁₆	C₂×C₃	semidirect
33. C₂×C₅×SD₃₂	C₂×C₃	semidirect
34. C₂×#3960	C₂×C₃	semidirect
35. C₂×#3959	C₂×C₃	semidirect
36. D₅×SD₃₂	C₂×C₃	direct (N × H)
37. C₂×#3932	C₂×C₃	semidirect
38. C₂×D₅×C₁₆	C₂×C₃	semidirect
53. C₃×C₅×Q₁₆	C₂³	semidirect
61. C₃×Dic₂₀	C₂³	semidirect
66. C₃×C₅×C₁₆	C₂³	semidirect
67. C₃×#672	C₂³	semidirect
74. C₂×C₃×SD₃₂	D₅	direct (N × H)
78. C₂×C₅×Q₁₆	C₂²×C₃	semidirect
83. D₅×Q₁₆	C₂²×C₃	semidirect
86. C₂×Dic₂₀	C₂²×C₃	semidirect
89. C₅×SD₃₂	C₂²×C₃	semidirect
90. C₂×C₅×C₁₆	C₂²×C₃	semidirect
91. #3960	C₂²×C₃	semidirect
92. #3959	C₂²×C₃	semidirect
93. C₂×#672	C₂²×C₃	semidirect
94. #3932	C₂²×C₃	semidirect
95. D₅×C₁₆	C₂²×C₃	semidirect
128. C₂×C₃×Q₁₆	C₂×D₅	semidirect
138. C₃×SD₃₂	C₂×D₅	direct (N × H)
141. C₂×C₃×C₁₆	C₂×D₅	semidirect
156. C₅×Q₁₆	C₂³×C₃	semidirect
164. Dic₂₀	C₂³×C₃	semidirect
169. C₅×C₁₆	C₂³×C₃	semidirect
170. #672	C₂³×C₃	semidirect
177. C₂×SD₃₂	C₃×D₅	direct (N × H)
185. C₂×C₃×D₅	SD₃₂	direct (N × H)
209. C₃×Q₁₆	C₂²×D₅	semidirect
220. C₃×C₁₆	C₂²×D₅	semidirect
252. C₂×Q₁₆	C₂×C₃×D₅	semidirect
262. SD₃₂	C₂×C₃×D₅	direct (N × H)
265. C₂×C₁₆	C₂×C₃×D₅	semidirect
267. C₂×C₃×C₅	C₂×SD₃₂	semidirect
270. C₃×D₅	C₂×SD₃₂	direct (N × H)
302. C₂×D₅	C₃×SD₃₂	direct (N × H)
326. Q₁₆	C₂²×C₃×D₅	semidirect
337. C₁₆	C₂²×C₃×D₅	semidirect
338. C₃×C₅	C₂²×SD₃₂	semidirect
353. C₂×C₅	C₂×C₃×SD₃₂	semidirect
356. D₅	C₂×C₃×SD₃₂	direct (N × H)
385. C₂×C₃	D₅×SD₃₂	direct (N × H)
387. C₅	C₂²×C₃×SD₃₂	semidirect
401. C₃	C₂×D₅×SD₃₂	direct (N × H)
405. C₂	C₃×D₅×SD₃₂	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃×D₅×Q₁₆	2
C₂×C₃×D₅×D₈	2
C₂×C₃×C₅×SD₃₂	2
C₂×C₃×#3960	2
C₂×C₃×#3959	2
C₃×D₅×SD₃₂	2
C₂×C₃×#3932	2
C₂×C₃×D₅×C₁₆	2
C₂×D₅×SD₃₂	3
C₂²×C₃×SD₃₂	5

Subgroups — C2×C3×D5×SD32 #14478214

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×D₅×SD₃₂ #14478214