Subgroups — C₂×C₅×D₃×SD₃₂ #14478213

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×C₅×D₃×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₅×D₃×D₈	C₂	1	1	yes	maximal, characteristic
3	C₂×C₃×C₅×SD₃₂	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₅×#828	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₅×#827	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×D₃×SD₃₂	C₂	1	8	yes	maximal, direct product factor
7	C₂×C₅×#800	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₅×D₃×C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×C₅×SD₃₂	—	3	1	no	maximal, Hall
10	C₂×C₅×D₃×Q₈	—	2	1	no	—
11	C₂×C₅×D₃×D₄	—	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×C₅×#216	—	2	1	no	—
15	C₂×C₅×#213	—	2	1	no	—
16	C₅×D₃×Q₁₆	—	2	2	no	—
17	C₅×D₃×Q₁₆	C₂²	1	4	yes	complemented
18	C₅×D₃×D₈	—	2	2	no	—
19	C₅×D₃×D₈	C₂²	1	4	yes	—
20	C₂×C₅×Dic₁₂	C₂²	1	1	yes	characteristic, complemented
21	C₂×C₅×D₂₄	C₂²	1	1	yes	characteristic
22	C₂×C₅×D₃×C₈	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	C₅×#828	C₂²	1	4	yes	complemented
26	C₅×#827	C₂²	1	4	yes	complemented
27	C₂×C₅×C₃⋊C₁₆	C₂²	1	1	yes	characteristic, complemented
28	C₅×#800	C₂²	1	4	yes	complemented
29	C₅×D₃×C₁₆	C₂²	1	4	yes	complemented
30	C₂×D₃×SD₃₂	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
31	C₂²×C₅×Q₁₆	—	3	1	no	—
32	C₂²×C₅×D₈	—	3	1	no	—
33	C₂×C₅×SD₃₂	—	3	8	no	—
34	C₂×C₅×SD₃₂	—	3	1	no	—
35	C₂×C₅×SD₃₂	—	3	1	no	—
36	C₂×C₅×SD₃₂	—	3	1	no	—
37	C₂×C₅×SD₃₂	D₃	1	1	yes	characteristic, direct product factor
38	C₂²×C₅×C₁₆	—	3	1	no	—
39	C₂³×C₅×D₃	—	4	1	no	—
40	C₂×C₃×C₅×Q₈	—	2	1	no	—
41	C₂×C₃×C₅×D₄	—	2	1	no	—
42	C₂×C₅×#67	—	4	1	no	—
43	C₅×D₃×Q₈	—	2	4	no	—
44	C₅×D₃×Q₈	—	4	2	no	—
45	C₅×D₃×D₄	—	2	4	no	—
46	C₅×D₃×D₄	—	4	2	no	—
47	C₂×C₅×D₁₂	—	2	1	no	—
48	C₂×C₄×C₅×D₃	—	4	1	no	—
49	C₂×C₄×C₅×D₃	D₄	1	1	yes	characteristic
50	C₂×C₅×Dic₆	—	2	1	no	—
51	C₂×C₅×Dic₆	—	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	C₅×#216	—	2	4	no	—
58	C₅×#213	—	2	4	no	—
59	C₂×C₅×C₃⋊C₈	D₄	1	1	yes	characteristic
60	C₅×Dic₁₂	—	2	1	no	—
61	C₅×Dic₁₂	C₂³	1	2	yes	complemented
62	C₅×D₂₄	—	2	1	no	—
63	C₅×D₂₄	C₂³	1	2	yes	—
64	C₅×D₃×C₈	D₄	1	2	yes	—
65	C₅×D₃×C₈	C₂³	1	2	yes	—
66	C₃×C₅×C₁₆	C₂³	1	2	yes	complemented
67	C₅×C₃⋊C₁₆	C₂³	1	2	yes	complemented
68	C₂×D₃×Q₁₆	C₂×C₅	1	1	yes	characteristic, complemented
69	C₂×D₃×D₈	C₂×C₅	1	1	yes	characteristic
70	C₂×C₃×SD₃₂	C₂×C₅	1	1	yes	characteristic, complemented
71	C₂×#828	C₂×C₅	1	1	yes	characteristic, complemented
72	C₂×#827	C₂×C₅	1	1	yes	characteristic, complemented
73	D₃×SD₃₂	C₂×C₅	1	8	yes	direct product factor
74	C₂×#800	C₂×C₅	1	1	yes	characteristic, complemented
75	C₂×D₃×C₁₆	C₂×C₅	1	1	yes	characteristic, complemented
76	C₂²×C₅×Q₈	—	6	1	no	—
77	C₂²×C₅×D₄	—	6	1	no	—
78	C₂×C₅×Q₁₆	—	3	4	no	—
79	C₂×C₅×Q₁₆	—	3	1	no	—
80	C₂×C₅×Q₁₆	—	6	2	no	—
81	C₂×C₅×Q₁₆	—	6	1	no	—
82	C₂×C₅×Q₁₆	C₂×D₃	1	1	yes	characteristic, complemented
83	C₂×C₅×D₈	—	3	4	no	—
84	C₂×C₅×D₈	—	3	1	no	—
85	C₂×C₅×D₈	—	6	2	no	—
86	C₂×C₅×D₈	—	6	1	no	—
87	C₂×C₅×D₈	C₂×D₃	1	1	yes	characteristic
88	C₂²×C₅×C₈	—	3	1	no	—
89	C₅×SD₃₂	—	3	4	no	—
90	C₅×SD₃₂	—	3	4	no	—
91	C₅×SD₃₂	—	3	4	no	—
92	C₅×SD₃₂	C₂×D₃	1	4	yes	direct product factor
93	C₂×C₅×C₁₆	—	3	1	no	—
94	C₂×C₅×C₁₆	—	3	4	no	—
95	C₂×C₅×C₁₆	C₂×D₃	1	1	yes	characteristic, complemented
96	C₂²×SD₃₂	—	3	1	no	Sylow
97	C₂³×C₃×C₅	—	4	1	no	—
98	C₂²×C₅×D₃	—	4	1	no	—
99	C₂²×C₅×D₃	—	4	4	no	—
100	C₂²×C₅×D₃	—	8	4	no	—
101	C₂²×C₅×D₃	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	C₅×#67	—	4	4	no	—
109	C₂×C₅×Dic₃	—	4	1	no	—
110	C₂×C₅×Dic₃	D₈	1	1	yes	characteristic
111	C₅×D₁₂	—	2	2	no	—
112	C₅×D₁₂	—	4	1	no	—
113	C₄×C₅×D₃	—	4	4	no	—
114	C₄×C₅×D₃	D₈	1	2	yes	—
115	C₄×C₅×D₃	C₂×D₄	1	2	yes	—
116	C₅×Dic₆	—	2	2	no	—
117	C₅×Dic₆	—	4	1	no	—
118	C₅×Dic₆	—	4	4	no	—
119	C₃×C₅×C₈	C₂×D₄	1	1	yes	characteristic
120	C₃×C₅×C₈	C₂⁴	1	1	yes	characteristic
121	C₅×C₃⋊C₈	C₂×D₄	1	2	yes	—
122	C₂×D₃×Q₈	—	2	1	no	—
123	C₂×D₃×D₄	—	2	1	no	—
124	C₂×C₃×Q₁₆	C₂²×C₅	1	1	yes	characteristic, complemented
125	C₂×C₃×D₈	C₂²×C₅	1	1	yes	characteristic
126	C₂×#216	—	2	1	no	—
127	C₂×#213	—	2	1	no	—
128	D₃×Q₁₆	—	2	2	no	—
129	D₃×Q₁₆	C₂²×C₅	1	4	yes	complemented
130	D₃×D₈	—	2	2	no	—
131	D₃×D₈	C₂²×C₅	1	4	yes	—
132	C₂×Dic₁₂	C₂²×C₅	1	1	yes	characteristic, complemented
133	C₂×D₂₄	C₂²×C₅	1	1	yes	characteristic
134	C₂×D₃×C₈	C₂²×C₅	1	1	yes	characteristic
135	C₃×SD₃₂	C₂²×C₅	1	4	yes	complemented
136	C₂×C₃×C₁₆	C₂²×C₅	1	1	yes	characteristic, complemented
137	#828	C₂²×C₅	1	4	yes	complemented
138	#827	C₂²×C₅	1	4	yes	complemented
139	C₂×C₃⋊C₁₆	C₂²×C₅	1	1	yes	characteristic, complemented
140	#800	C₂²×C₅	1	4	yes	complemented
141	D₃×C₁₆	C₂²×C₅	1	4	yes	complemented
142	C₂⁴×C₅	—	12	1	no	—
143	C₂×C₅×Q₈	—	2	1	no	—
144	C₂×C₅×Q₈	—	6	4	no	—
145	C₂×C₅×Q₈	—	6	1	no	—
146	C₂×C₅×Q₈	—	12	1	no	—
147	C₂×C₅×Q₈	—	12	2	no	—
148	C₂×C₅×D₄	—	2	1	no	—
149	C₂×C₅×D₄	—	6	4	no	—
150	C₂×C₅×D₄	—	6	1	no	—
151	C₂×C₅×D₄	—	12	2	no	—
152	C₂×C₅×D₄	—	12	1	no	—
153	C₂²×C₄×C₅	—	3	1	no	—
154	C₂²×C₄×C₅	—	12	1	no	—
155	C₅×Q₁₆	—	2	1	no	—
156	C₅×Q₁₆	—	3	2	no	—
157	C₅×Q₁₆	—	6	4	no	—
158	C₅×Q₁₆	—	6	1	no	—
159	C₅×Q₁₆	C₂²×D₃	1	2	yes	complemented
160	C₅×D₈	—	2	1	no	—
161	C₅×D₈	—	3	2	no	—
162	C₅×D₈	—	6	4	no	—
163	C₅×D₈	—	6	1	no	—
164	C₅×D₈	C₂²×D₃	1	2	yes	—
165	C₂×C₅×C₈	—	3	1	no	—
166	C₂×C₅×C₈	—	3	2	no	—
167	C₂×C₅×C₈	—	3	2	no	—
168	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
169	C₅×C₁₆	—	3	2	no	—
170	C₅×C₁₆	C₂²×D₃	1	2	yes	complemented
171	C₂²×Q₁₆	—	3	1	no	—
172	C₂²×D₈	—	3	1	no	—
173	C₂×SD₃₂	—	3	1	no	—
174	C₂×SD₃₂	—	3	1	no	—
175	C₂×SD₃₂	—	3	8	no	—
176	C₂×SD₃₂	—	3	1	no	—
177	C₂×SD₃₂	C₅×D₃	1	1	yes	characteristic, direct product factor
178	C₂²×C₁₆	—	3	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×C₅×D₃	—	4	2	no	—
183	C₂×C₅×D₃	—	8	2	no	—
184	C₂×C₅×D₃	—	8	8	no	—
185	C₂×C₅×D₃	SD₃₂	1	4	yes	direct product factor
186	C₂×C₅×D₃	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	C₅×Dic₃	—	4	2	no	—
191	C₅×Dic₃	C₂×D₈	1	2	yes	—
192	C₂³×D₃	—	4	1	no	—
193	C₂×C₃×Q₈	—	2	1	no	—
194	C₂×C₃×D₄	—	2	1	no	—
195	C₂×#67	—	4	1	no	—
196	D₃×Q₈	—	2	4	no	—
197	D₃×Q₈	—	4	2	no	—
198	D₃×D₄	—	2	4	no	—
199	D₃×D₄	—	4	2	no	—
200	C₂×D₁₂	—	2	1	no	—
201	C₂×C₄×D₃	—	4	1	no	—
202	C₂×C₄×D₃	C₅×D₄	1	1	yes	characteristic
203	C₂×Dic₆	—	2	1	no	—
204	C₂×Dic₆	—	4	1	no	—
205	C₃×Q₁₆	—	2	1	no	—
206	C₃×Q₁₆	C₂³×C₅	1	2	yes	complemented
207	C₃×D₈	—	2	1	no	—
208	C₃×D₈	C₂³×C₅	1	2	yes	—
209	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
210	#216	—	2	4	no	—
211	#213	—	2	4	no	—
212	C₂×C₃⋊C₈	C₅×D₄	1	1	yes	characteristic
213	Dic₁₂	—	2	1	no	—
214	Dic₁₂	C₂³×C₅	1	2	yes	complemented
215	D₂₄	—	2	1	no	—
216	D₂₄	C₂³×C₅	1	2	yes	—
217	D₃×C₈	C₅×D₄	1	2	yes	—
218	D₃×C₈	C₂³×C₅	1	2	yes	—
219	C₃×C₁₆	C₂³×C₅	1	2	yes	complemented
220	C₃⋊C₁₆	C₂³×C₅	1	2	yes	complemented
221	C₂³×C₅	—	3	1	no	—
222	C₂³×C₅	—	4	1	no	—
223	C₂³×C₅	—	12	4	no	—
224	C₂³×C₅	—	12	1	no	—
225	C₂³×C₅	—	24	4	no	—
226	C₅×Q₈	—	2	2	no	—
227	C₅×Q₈	—	4	1	no	—
228	C₅×Q₈	—	6	2	no	—
229	C₅×Q₈	—	12	4	no	—
230	C₅×Q₈	—	12	1	no	—
231	C₅×D₄	—	2	2	no	—
232	C₅×D₄	—	4	1	no	—
233	C₅×D₄	—	6	2	no	—
234	C₅×D₄	—	12	4	no	—
235	C₅×D₄	—	12	1	no	—
236	C₂×C₄×C₅	—	3	1	no	—
237	C₂×C₄×C₅	—	3	2	no	—
238	C₂×C₄×C₅	—	3	2	no	—
239	C₂×C₄×C₅	—	4	1	no	—
240	C₂×C₄×C₅	—	12	4	no	—
241	C₂×C₄×C₅	—	12	1	no	—
242	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
243	C₅×C₈	—	3	2	no	—
244	C₅×C₈	D₃×D₄	1	1	yes	characteristic
245	C₅×C₈	C₂³×D₃	1	1	yes	characteristic
246	C₂²×Q₈	—	6	1	no	—
247	C₂²×D₄	—	6	1	no	—
248	C₂×Q₁₆	—	3	4	no	—
249	C₂×Q₁₆	—	3	1	no	—
250	C₂×Q₁₆	—	6	2	no	—
251	C₂×Q₁₆	—	6	1	no	—
252	C₂×Q₁₆	C₂×C₅×D₃	1	1	yes	characteristic, complemented
253	C₂×D₈	—	3	4	no	—
254	C₂×D₈	—	3	1	no	—
255	C₂×D₈	—	6	2	no	—
256	C₂×D₈	—	6	1	no	—
257	C₂×D₈	C₂×C₅×D₃	1	1	yes	characteristic
258	C₂²×C₈	—	3	1	no	—
259	SD₃₂	—	3	4	no	—
260	SD₃₂	—	3	4	no	—
261	SD₃₂	—	3	4	no	—
262	SD₃₂	C₂×C₅×D₃	1	4	yes	direct product factor
263	C₂×C₁₆	—	3	1	no	—
264	C₂×C₁₆	—	3	4	no	—
265	C₂×C₁₆	C₂×C₅×D₃	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	C₅×D₃	—	8	2	no	—
270	C₅×D₃	C₂×SD₃₂	1	4	yes	direct product factor
271	C₂³×C₃	—	4	1	no	—
272	C₂²×D₃	—	4	1	no	—
273	C₂²×D₃	—	4	4	no	—
274	C₂²×D₃	—	8	4	no	—
275	C₂²×D₃	C₅×D₈	1	1	yes	characteristic
276	C₃×Q₈	—	2	2	no	—
277	C₃×Q₈	—	4	1	no	—
278	C₃×D₄	—	2	2	no	—
279	C₃×D₄	—	4	1	no	—
280	C₂×C₃×C₄	—	4	1	no	—
281	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
282	#67	—	4	4	no	—
283	C₂×Dic₃	—	4	1	no	—
284	C₂×Dic₃	C₅×D₈	1	1	yes	characteristic
285	D₁₂	—	2	2	no	—
286	D₁₂	—	4	1	no	—
287	C₄×D₃	—	4	4	no	—
288	C₄×D₃	C₅×D₈	1	2	yes	—
289	C₄×D₃	C₂×C₅×D₄	1	2	yes	—
290	Dic₆	—	2	2	no	—
291	Dic₆	—	4	1	no	—
292	Dic₆	—	4	4	no	—
293	C₃×C₈	C₂×C₅×D₄	1	1	yes	characteristic
294	C₃×C₈	C₂⁴×C₅	1	1	yes	characteristic
295	C₃⋊C₈	C₂×C₅×D₄	1	2	yes	—
296	C₂²×C₅	—	3	4	no	—
297	C₂²×C₅	—	3	2	no	—
298	C₂²×C₅	—	4	2	no	—
299	C₂²×C₅	—	8	2	no	—
300	C₂²×C₅	—	12	2	no	—
301	C₂²×C₅	—	24	8	no	—
302	C₂²×C₅	—	24	2	no	—
303	C₂²×C₅	D₃×D₈	1	1	yes	characteristic
304	C₄×C₅	—	3	2	no	—
305	C₄×C₅	—	4	2	no	—
306	C₄×C₅	—	12	2	no	—
307	C₄×C₅	D₃×D₈	1	1	yes	characteristic
308	C₄×C₅	C₂×D₃×D₄	1	1	yes	characteristic
309	C₂⁴	—	12	1	no	—
310	C₂×Q₈	—	2	1	no	—
311	C₂×Q₈	—	6	4	no	—
312	C₂×Q₈	—	6	1	no	—
313	C₂×Q₈	—	12	1	no	—
314	C₂×Q₈	—	12	2	no	—
315	C₂×D₄	—	2	1	no	—
316	C₂×D₄	—	6	4	no	—
317	C₂×D₄	—	6	1	no	—
318	C₂×D₄	—	12	2	no	—
319	C₂×D₄	—	12	1	no	—
320	C₂²×C₄	—	3	1	no	—
321	C₂²×C₄	—	12	1	no	—
322	Q₁₆	—	2	1	no	—
323	Q₁₆	—	3	2	no	—
324	Q₁₆	—	6	4	no	—
325	Q₁₆	—	6	1	no	—
326	Q₁₆	C₂²×C₅×D₃	1	2	yes	complemented
327	D₈	—	2	1	no	—
328	D₈	—	3	2	no	—
329	D₈	—	6	4	no	—
330	D₈	—	6	1	no	—
331	D₈	C₂²×C₅×D₃	1	2	yes	—
332	C₂×C₈	—	3	1	no	—
333	C₂×C₈	—	3	2	no	—
334	C₂×C₈	—	3	2	no	—
335	C₂×C₈	C₂²×C₅×D₃	1	1	yes	characteristic
336	C₁₆	—	3	2	no	—
337	C₁₆	C₂²×C₅×D₃	1	2	yes	complemented
338	C₃×C₅	C₂²×SD₃₂	1	1	yes	characteristic, complemented, Hall
339	C₂²×C₃	—	4	2	no	—
340	C₂²×C₃	—	8	2	no	—
341	C₂²×C₃	C₂×C₅×D₈	1	1	yes	characteristic
342	C₂×D₃	—	4	2	no	—
343	C₂×D₃	—	8	2	no	—
344	C₂×D₃	—	8	8	no	—
345	C₂×D₃	C₅×SD₃₂	1	4	yes	direct product factor
346	C₂×D₃	C₂×C₅×D₈	1	2	yes	—
347	C₃×C₄	—	4	2	no	—
348	C₃×C₄	C₂×C₅×D₈	1	1	yes	characteristic
349	C₃×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
350	Dic₃	—	4	2	no	—
351	Dic₃	C₂×C₅×D₈	1	2	yes	—
352	C₂×C₅	—	3	4	no	—
353	C₂×C₅	—	8	2	no	—
354	C₂×C₅	—	24	2	no	—
355	C₂×C₅	D₃×SD₃₂	1	2	yes	direct product factor
356	C₂×C₅	C₂×D₃×D₈	1	1	yes	characteristic
357	C₂³	—	3	1	no	—
358	C₂³	—	4	1	no	—
359	C₂³	—	12	4	no	—
360	C₂³	—	12	1	no	—
361	C₂³	—	24	4	no	—
362	Q₈	—	2	2	no	—
363	Q₈	—	4	1	no	—
364	Q₈	—	6	2	no	—
365	Q₈	—	12	4	no	—
366	Q₈	—	12	1	no	—
367	D₄	—	2	2	no	—
368	D₄	—	4	1	no	—
369	D₄	—	6	2	no	—
370	D₄	—	12	4	no	—
371	D₄	—	12	1	no	—
372	C₂×C₄	—	3	1	no	—
373	C₂×C₄	—	3	2	no	—
374	C₂×C₄	—	3	2	no	—
375	C₂×C₄	—	4	1	no	—
376	C₂×C₄	—	12	4	no	—
377	C₂×C₄	—	12	1	no	—
378	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
379	C₈	—	3	2	no	—
380	C₈	C₅×D₃×D₄	1	1	yes	characteristic
381	C₈	C₂³×C₅×D₃	1	1	yes	characteristic
382	C₂×C₃	—	8	2	no	—
383	C₂×C₃	C₂×C₅×SD₃₂	1	2	yes	complemented
384	C₂×C₃	C₂²×C₅×D₈	1	1	yes	characteristic
385	D₃	—	8	2	no	—
386	D₃	C₂×C₅×SD₃₂	1	4	yes	direct product factor
387	C₅	C₂×D₃×SD₃₂	1	1	yes	characteristic, direct product factor, Sylow
388	C₂²	—	3	4	no	—
389	C₂²	—	3	2	no	—
390	C₂²	—	4	2	no	—
391	C₂²	—	8	2	no	—
392	C₂²	—	12	2	no	—
393	C₂²	—	24	8	no	—
394	C₂²	—	24	2	no	—
395	C₂²	C₅×D₃×D₈	1	1	yes	characteristic
396	C₄	—	3	2	no	—
397	C₄	—	4	2	no	—
398	C₄	—	12	2	no	—
399	C₄	C₅×D₃×D₈	1	1	yes	characteristic
400	C₄	C₂×C₅×D₃×D₄	1	1	yes	characteristic
401	C₃	C₂²×C₅×SD₃₂	1	1	yes	characteristic, complemented, Sylow
402	C₂	—	3	4	no	—
403	C₂	—	8	2	no	—
404	C₂	—	24	2	no	—
405	C₂	C₅×D₃×SD₃₂	1	2	yes	direct product factor
406	C₂	C₂×C₅×D₃×D₈	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₅	D₃×D₈
commutator, cosocle	C₃×C₈	C₂⁴×C₅
Frattini	C₈	C₂³×C₅×D₃
Fitting	C₂×C₃×C₅×SD₃₂	C₂
socle	C₂²×C₃×C₅	C₂×D₈
prime radical	C₂×C₅×D₃×D₈	C₂
hypercenter	C₂×C₅×SD₃₂	D₃
hypocenter	C₃	C₂²×C₅×SD₃₂
LCS	G ▷ C₃×C₈ ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₂×C₄×C₅ ◁ C₂×C₅×C₈ ◁ C₂×C₅×SD₃₂

Complements

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

N	H ≅ G/N	type
1. C₂×C₅×D₃×Q₁₆	C₂	semidirect
3. C₂×C₃×C₅×SD₃₂	C₂	semidirect
4. C₂×C₅×#828	C₂	semidirect
5. C₂×C₅×#827	C₂	semidirect
6. C₅×D₃×SD₃₂	C₂	direct (N × H)
7. C₂×C₅×#800	C₂	semidirect
8. C₂×C₅×D₃×C₁₆	C₂	semidirect
12. C₂×C₃×C₅×Q₁₆	C₂²	semidirect
17. C₅×D₃×Q₁₆	C₂²	semidirect
20. C₂×C₅×Dic₁₂	C₂²	semidirect
23. C₃×C₅×SD₃₂	C₂²	semidirect
24. C₂×C₃×C₅×C₁₆	C₂²	semidirect
25. C₅×#828	C₂²	semidirect
26. C₅×#827	C₂²	semidirect
27. C₂×C₅×C₃⋊C₁₆	C₂²	semidirect
28. C₅×#800	C₂²	semidirect
29. C₅×D₃×C₁₆	C₂²	semidirect
30. C₂×D₃×SD₃₂	C₅	direct (N × H)
37. C₂×C₅×SD₃₂	D₃	direct (N × H)
53. C₃×C₅×Q₁₆	C₂³	semidirect
61. C₅×Dic₁₂	C₂³	semidirect
66. C₃×C₅×C₁₆	C₂³	semidirect
67. C₅×C₃⋊C₁₆	C₂³	semidirect
68. C₂×D₃×Q₁₆	C₂×C₅	semidirect
70. C₂×C₃×SD₃₂	C₂×C₅	semidirect
71. C₂×#828	C₂×C₅	semidirect
72. C₂×#827	C₂×C₅	semidirect
73. D₃×SD₃₂	C₂×C₅	direct (N × H)
74. C₂×#800	C₂×C₅	semidirect
75. C₂×D₃×C₁₆	C₂×C₅	semidirect
82. C₂×C₅×Q₁₆	C₂×D₃	semidirect
92. C₅×SD₃₂	C₂×D₃	direct (N × H)
95. C₂×C₅×C₁₆	C₂×D₃	semidirect
124. C₂×C₃×Q₁₆	C₂²×C₅	semidirect
129. D₃×Q₁₆	C₂²×C₅	semidirect
132. C₂×Dic₁₂	C₂²×C₅	semidirect
135. C₃×SD₃₂	C₂²×C₅	semidirect
136. C₂×C₃×C₁₆	C₂²×C₅	semidirect
137. #828	C₂²×C₅	semidirect
138. #827	C₂²×C₅	semidirect
139. C₂×C₃⋊C₁₆	C₂²×C₅	semidirect
140. #800	C₂²×C₅	semidirect
141. D₃×C₁₆	C₂²×C₅	semidirect
159. C₅×Q₁₆	C₂²×D₃	semidirect
170. C₅×C₁₆	C₂²×D₃	semidirect
177. C₂×SD₃₂	C₅×D₃	direct (N × H)
185. C₂×C₅×D₃	SD₃₂	direct (N × H)
206. C₃×Q₁₆	C₂³×C₅	semidirect
214. Dic₁₂	C₂³×C₅	semidirect
219. C₃×C₁₆	C₂³×C₅	semidirect
220. C₃⋊C₁₆	C₂³×C₅	semidirect
252. C₂×Q₁₆	C₂×C₅×D₃	semidirect
262. SD₃₂	C₂×C₅×D₃	direct (N × H)
265. C₂×C₁₆	C₂×C₅×D₃	semidirect
267. C₂×C₃×C₅	C₂×SD₃₂	semidirect
270. C₅×D₃	C₂×SD₃₂	direct (N × H)
326. Q₁₆	C₂²×C₅×D₃	semidirect
337. C₁₆	C₂²×C₅×D₃	semidirect
338. C₃×C₅	C₂²×SD₃₂	semidirect
345. C₂×D₃	C₅×SD₃₂	direct (N × H)
355. C₂×C₅	D₃×SD₃₂	direct (N × H)
383. C₂×C₃	C₂×C₅×SD₃₂	semidirect
386. D₃	C₂×C₅×SD₃₂	direct (N × H)
387. C₅	C₂×D₃×SD₃₂	direct (N × H)
401. C₃	C₂²×C₅×SD₃₂	semidirect
405. C₂	C₅×D₃×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×C₅×D₃×Q₁₆	2
C₂×C₅×D₃×D₈	2
C₂×C₃×C₅×SD₃₂	2
C₂×C₅×#828	2
C₂×C₅×#827	2
C₅×D₃×SD₃₂	2
C₂×C₅×#800	2
C₂×C₅×D₃×C₁₆	2
C₂²×C₅×SD₃₂	3
C₂×D₃×SD₃₂	5

Subgroups — C2×C5×D3×SD32 #14478213

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×D₃×SD₃₂ #14478213