Subgroups — C₅×D₃×#492 #14438721

Order 1920.

1312 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×D₃×SD₁₆	C₂	1	4	yes	maximal, complemented
2	C₅×D₃×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×D₃×#127	C₂	1	1	yes	maximal, characteristic
4	C₃×C₅×#492	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#5175	C₂	1	4	yes	maximal, complemented
6	C₅×#5085	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#5076	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#4693	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄×C₅×D₃×C₈	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₅×#492	—	3	1	no	maximal, Hall
11	C₂×C₅×D₃×Q₈	C₂²	1	2	yes	—
12	C₂×C₅×D₃×D₄	—	2	2	no	—
13	C₂×C₅×D₃×D₄	C₂²	1	2	yes	—
14	C₂×C₃×C₅×SD₁₆	C₂²	1	4	yes	complemented
15	C₃×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
16	C₃×C₅×#127	C₂²	1	1	yes	characteristic
17	C₅×#944	C₂²	1	2	yes	complemented
18	C₂×C₅×#215	C₂²	1	4	yes	complemented
19	C₅×#940	—	2	2	no	—
20	C₅×#940	C₂²	1	2	yes	—
21	C₂×C₅×#214	C₂²	1	4	yes	complemented
22	C₅×D₃×SD₁₆	—	2	16	no	—
23	C₂×C₅×#204	C₂²	1	4	yes	complemented
24	C₂×C₅×D₃×C₈	C₂²	1	2	yes	—
25	C₅×D₃×C₄⋊C₄	—	2	2	no	—
26	C₅×#888	—	2	2	no	—
27	C₅×#874	C₂²	1	1	yes	characteristic
28	C₄²×C₅×D₃	C₂²	1	1	yes	characteristic
29	C₅×#869	C₂²	1	1	yes	characteristic, complemented
30	C₃×C₄×C₅×C₈	C₂²	1	1	yes	characteristic, complemented
31	C₅×C₈×Dic₃	C₂²	1	2	yes	complemented
32	C₄×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic, complemented
33	D₃×#492	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
34	C₂²×C₅×SD₁₆	—	3	4	no	—
35	C₂×C₅×C₄⋊Q₈	—	3	1	no	—
36	C₂×C₅×#127	—	3	1	no	—
37	C₅×#492	—	3	1	no	—
38	C₅×#492	—	3	4	no	—
39	C₅×#492	—	3	1	no	—
40	C₅×#492	—	3	1	no	—
41	C₅×#492	D₃	1	1	yes	characteristic, direct product factor
42	C₂×C₄×C₅×C₈	—	3	1	no	—
43	C₂³×C₅×D₃	—	2	2	no	—
44	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
45	C₂×C₃×C₅×D₄	—	2	2	no	—
46	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
47	C₂×C₅×#67	—	2	2	no	—
48	C₂×C₅×#67	—	2	4	no	—
49	C₅×D₃×Q₈	—	2	8	no	—
50	C₅×D₃×D₄	—	2	8	no	—
51	C₅×D₃×D₄	—	4	8	no	—
52	C₂×C₅×D₁₂	—	2	2	no	—
53	C₂×C₅×D₁₂	C₂³	1	2	yes	—
54	C₂×C₄×C₅×D₃	—	2	2	no	—
55	C₂×C₄×C₅×D₃	D₄	1	2	yes	—
56	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
57	C₂×C₅×Dic₆	—	2	2	no	—
58	C₂×C₅×Dic₆	C₂³	1	2	yes	—
59	C₃×C₅×SD₁₆	—	2	8	no	—
60	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
61	C₃×C₅×C₄⋊C₄	—	2	2	no	—
62	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
63	C₅×#215	—	2	8	no	—
64	C₅×#214	—	2	8	no	—
65	C₅×C₄⋊Dic₃	—	2	2	no	—
66	C₅×Dic₃⋊C₄	—	2	4	no	—
67	C₄×C₅×Dic₃	D₄	1	2	yes	—
68	C₄×C₅×Dic₃	C₂³	1	1	yes	characteristic
69	C₂×C₅×C₃⋊C₈	C₂³	1	2	yes	—
70	C₅×#204	—	2	8	no	—
71	C₅×D₃×C₈	D₄	1	8	yes	complemented
72	C₂×D₃×SD₁₆	C₂×C₅	1	4	yes	complemented
73	D₃×C₄⋊Q₈	C₂×C₅	1	1	yes	characteristic, complemented
74	D₃×#127	C₂×C₅	1	1	yes	characteristic
75	C₃×#492	C₂×C₅	1	1	yes	characteristic, complemented
76	#5175	C₂×C₅	1	4	yes	complemented
77	#5085	C₂×C₅	1	1	yes	characteristic, complemented
78	#5076	C₂×C₅	1	1	yes	characteristic, complemented
79	#4693	C₂×C₅	1	1	yes	characteristic, complemented
80	C₄×D₃×C₈	C₂×C₅	1	1	yes	characteristic, complemented
81	C₂²×C₅×Q₈	—	3	2	no	—
82	C₂²×C₅×D₄	—	3	2	no	—
83	C₂²×C₅×D₄	—	6	2	no	—
84	C₂×C₅×SD₁₆	—	3	4	no	—
85	C₂×C₅×SD₁₆	—	3	4	no	—
86	C₂×C₅×SD₁₆	—	3	4	no	—
87	C₂×C₅×SD₁₆	—	6	16	no	—
88	C₂×C₅×SD₁₆	C₂×D₃	1	4	yes	complemented
89	C₂²×C₅×C₈	—	3	2	no	—
90	C₅×C₄⋊Q₈	—	3	2	no	—
91	C₅×C₄⋊Q₈	—	3	1	no	—
92	C₅×C₄⋊Q₈	—	6	2	no	—
93	C₅×C₄⋊Q₈	C₂×D₃	1	1	yes	characteristic, complemented
94	C₅×#127	—	3	2	no	—
95	C₅×#127	—	3	1	no	—
96	C₅×#127	—	6	2	no	—
97	C₅×#127	C₂×D₃	1	1	yes	characteristic
98	C₂×C₅×C₄⋊C₄	—	6	2	no	—
99	C₂×C₄²×C₅	—	3	1	no	—
100	C₄×C₅×C₈	—	3	2	no	—
101	C₄×C₅×C₈	—	3	1	no	—
102	C₄×C₅×C₈	C₂×D₃	1	1	yes	characteristic, complemented
103	C₂×#492	—	3	1	no	Sylow
104	C₂³×C₃×C₅	—	2	2	no	—
105	C₂²×C₅×D₃	—	2	2	no	—
106	C₂²×C₅×D₃	—	4	4	no	—
107	C₂²×C₅×D₃	—	4	8	no	—
108	C₂²×C₅×D₃	C₂×D₄	1	1	yes	characteristic
109	C₃×C₅×Q₈	—	2	4	no	—
110	C₃×C₅×D₄	—	2	4	no	—
111	C₃×C₅×D₄	—	4	4	no	—
112	C₂×C₃×C₄×C₅	—	2	2	no	—
113	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
114	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
115	C₅×#67	—	4	4	no	—
116	C₅×#67	—	4	8	no	—
117	C₂×C₅×Dic₃	—	2	2	no	—
118	C₂×C₅×Dic₃	C₂×D₄	1	1	yes	characteristic
119	C₂×C₅×Dic₃	C₂×D₄	1	2	yes	—
120	C₅×D₁₂	—	2	4	no	—
121	C₅×D₁₂	—	4	4	no	—
122	C₄×C₅×D₃	—	4	4	no	—
123	C₄×C₅×D₃	SD₁₆	1	8	yes	complemented
124	C₄×C₅×D₃	C₂×D₄	1	4	yes	—
125	C₅×Dic₆	—	2	4	no	—
126	C₅×Dic₆	—	4	4	no	—
127	C₃×C₅×C₈	C₂×D₄	1	4	yes	complemented
128	C₅×C₃⋊C₈	C₂×D₄	1	4	yes	complemented
129	C₂×D₃×Q₈	C₂²×C₅	1	2	yes	—
130	C₂×D₃×D₄	—	2	2	no	—
131	C₂×D₃×D₄	C₂²×C₅	1	2	yes	—
132	C₂×C₃×SD₁₆	C₂²×C₅	1	4	yes	complemented
133	C₃×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic, complemented
134	C₃×#127	C₂²×C₅	1	1	yes	characteristic
135	#944	C₂²×C₅	1	2	yes	complemented
136	C₂×#215	C₂²×C₅	1	4	yes	complemented
137	#940	—	2	2	no	—
138	#940	C₂²×C₅	1	2	yes	—
139	C₂×#214	C₂²×C₅	1	4	yes	complemented
140	D₃×SD₁₆	—	2	16	no	—
141	C₂×#204	C₂²×C₅	1	4	yes	complemented
142	C₂×D₃×C₈	C₂²×C₅	1	2	yes	—
143	D₃×C₄⋊C₄	—	2	2	no	—
144	#888	—	2	2	no	—
145	#874	C₂²×C₅	1	1	yes	characteristic
146	C₄²×D₃	C₂²×C₅	1	1	yes	characteristic
147	#869	C₂²×C₅	1	1	yes	characteristic, complemented
148	C₃×C₄×C₈	C₂²×C₅	1	1	yes	characteristic, complemented
149	C₈×Dic₃	C₂²×C₅	1	2	yes	complemented
150	C₄×C₃⋊C₈	C₂²×C₅	1	1	yes	characteristic, complemented
151	C₂⁴×C₅	—	6	2	no	—
152	C₂×C₅×Q₈	—	3	2	no	—
153	C₂×C₅×Q₈	—	6	2	no	—
154	C₂×C₅×Q₈	—	6	8	no	—
155	C₂×C₅×Q₈	C₂²×D₃	1	2	yes	—
156	C₂×C₅×D₄	—	2	2	no	—
157	C₂×C₅×D₄	—	3	2	no	—
158	C₂×C₅×D₄	—	6	8	no	—
159	C₂×C₅×D₄	—	6	4	no	—
160	C₂×C₅×D₄	—	6	2	no	—
161	C₂×C₅×D₄	—	6	2	no	—
162	C₂×C₅×D₄	—	12	8	no	—
163	C₂×C₅×D₄	C₂²×D₃	1	2	yes	—
164	C₂²×C₄×C₅	—	3	2	no	—
165	C₂²×C₄×C₅	—	3	1	no	—
166	C₂²×C₄×C₅	—	6	2	no	—
167	C₅×SD₁₆	—	2	8	no	—
168	C₅×SD₁₆	—	6	8	no	—
169	C₅×SD₁₆	—	6	8	no	—
170	C₅×SD₁₆	—	6	8	no	—
171	C₂×C₅×C₈	—	3	2	no	—
172	C₂×C₅×C₈	—	3	8	no	—
173	C₂×C₅×C₈	C₂²×D₃	1	2	yes	—
174	C₅×C₄⋊C₄	—	2	2	no	—
175	C₅×C₄⋊C₄	—	6	4	no	—
176	C₅×C₄⋊C₄	—	6	2	no	—
177	C₄²×C₅	—	3	2	no	—
178	C₄²×C₅	—	3	1	no	—
179	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
180	C₂²×SD₁₆	—	3	4	no	—
181	C₂×C₄⋊Q₈	—	3	1	no	—
182	C₂×#127	—	3	1	no	—
183	#492	—	3	4	no	—
184	#492	—	3	1	no	—
185	#492	—	3	1	no	—
186	#492	—	3	1	no	—
187	#492	C₅×D₃	1	1	yes	characteristic, direct product factor
188	C₂×C₄×C₈	—	3	1	no	—
189	C₂²×C₃×C₅	—	4	2	no	—
190	C₂²×C₃×C₅	—	4	4	no	—
191	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
192	C₂×C₅×D₃	—	4	2	no	—
193	C₂×C₅×D₃	—	4	4	no	—
194	C₂×C₅×D₃	—	8	8	no	—
195	C₂×C₅×D₃	#127	1	2	yes	—
196	C₂×C₅×D₃	C₂×SD₁₆	1	4	yes	—
197	C₃×C₄×C₅	—	4	2	no	—
198	C₃×C₄×C₅	C₂×SD₁₆	1	4	yes	complemented
199	C₃×C₄×C₅	C₂²×D₄	1	2	yes	—
200	C₅×Dic₃	—	4	2	no	—
201	C₅×Dic₃	#127	1	2	yes	—
202	C₅×Dic₃	C₂×SD₁₆	1	4	yes	complemented
203	C₂³×D₃	—	2	2	no	—
204	C₂×C₃×Q₈	C₂³×C₅	1	2	yes	—
205	C₂×C₃×D₄	—	2	2	no	—
206	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
207	C₂×#67	—	2	2	no	—
208	C₂×#67	—	2	4	no	—
209	D₃×Q₈	—	2	8	no	—
210	D₃×D₄	—	2	8	no	—
211	D₃×D₄	—	4	8	no	—
212	C₂×D₁₂	—	2	2	no	—
213	C₂×D₁₂	C₂³×C₅	1	2	yes	—
214	C₂×C₄×D₃	—	2	2	no	—
215	C₂×C₄×D₃	C₅×D₄	1	2	yes	—
216	C₂×C₄×D₃	C₂³×C₅	1	1	yes	characteristic
217	C₂×Dic₆	—	2	2	no	—
218	C₂×Dic₆	C₂³×C₅	1	2	yes	—
219	C₃×SD₁₆	—	2	8	no	—
220	C₂×C₃×C₈	C₂³×C₅	1	2	yes	—
221	C₃×C₄⋊C₄	—	2	2	no	—
222	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
223	#215	—	2	8	no	—
224	#214	—	2	8	no	—
225	C₄⋊Dic₃	—	2	2	no	—
226	Dic₃⋊C₄	—	2	4	no	—
227	C₄×Dic₃	C₅×D₄	1	2	yes	—
228	C₄×Dic₃	C₂³×C₅	1	1	yes	characteristic
229	C₂×C₃⋊C₈	C₂³×C₅	1	2	yes	—
230	#204	—	2	8	no	—
231	D₃×C₈	C₅×D₄	1	8	yes	complemented
232	C₂³×C₅	—	2	2	no	—
233	C₂³×C₅	—	3	1	no	—
234	C₂³×C₅	—	6	2	no	—
235	C₂³×C₅	—	12	4	no	—
236	C₂³×C₅	—	12	8	no	—
237	C₅×Q₈	—	2	4	no	—
238	C₅×Q₈	—	6	4	no	—
239	C₅×Q₈	—	12	4	no	—
240	C₅×D₄	—	2	4	no	—
241	C₅×D₄	—	4	4	no	—
242	C₅×D₄	—	6	4	no	—
243	C₅×D₄	—	12	4	no	—
244	C₅×D₄	—	12	8	no	—
245	C₅×D₄	—	12	4	no	—
246	C₂×C₄×C₅	—	2	2	no	—
247	C₂×C₄×C₅	—	3	2	no	—
248	C₂×C₄×C₅	—	3	1	no	—
249	C₂×C₄×C₅	—	3	8	no	—
250	C₂×C₄×C₅	—	3	4	no	—
251	C₂×C₄×C₅	—	6	2	no	—
252	C₂×C₄×C₅	—	12	4	no	—
253	C₂×C₄×C₅	D₃×D₄	1	2	yes	—
254	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
255	C₅×C₈	—	3	4	no	—
256	C₅×C₈	D₃×D₄	1	4	yes	complemented
257	C₂²×Q₈	—	3	2	no	—
258	C₂²×D₄	—	3	2	no	—
259	C₂²×D₄	—	6	2	no	—
260	C₂×SD₁₆	—	3	4	no	—
261	C₂×SD₁₆	—	3	4	no	—
262	C₂×SD₁₆	—	3	4	no	—
263	C₂×SD₁₆	—	6	16	no	—
264	C₂×SD₁₆	C₂×C₅×D₃	1	4	yes	complemented
265	C₂²×C₈	—	3	2	no	—
266	C₄⋊Q₈	—	3	2	no	—
267	C₄⋊Q₈	—	3	1	no	—
268	C₄⋊Q₈	—	6	2	no	—
269	C₄⋊Q₈	C₂×C₅×D₃	1	1	yes	characteristic, complemented
270	#127	—	3	2	no	—
271	#127	—	3	1	no	—
272	#127	—	6	2	no	—
273	#127	C₂×C₅×D₃	1	1	yes	characteristic
274	C₂×C₄⋊C₄	—	6	2	no	—
275	C₂×C₄²	—	3	1	no	—
276	C₄×C₈	—	3	2	no	—
277	C₄×C₈	—	3	1	no	—
278	C₄×C₈	C₂×C₅×D₃	1	1	yes	characteristic, complemented
279	C₂×C₃×C₅	—	8	2	no	—
280	C₂×C₃×C₅	C₂×#127	1	1	yes	characteristic
281	C₂×C₃×C₅	C₂²×SD₁₆	1	2	yes	—
282	C₅×D₃	—	8	2	no	—
283	C₅×D₃	#492	1	4	yes	direct product factor
284	C₂³×C₃	—	2	2	no	—
285	C₂²×D₃	—	2	2	no	—
286	C₂²×D₃	—	4	4	no	—
287	C₂²×D₃	—	4	8	no	—
288	C₂²×D₃	C₂×C₅×D₄	1	1	yes	characteristic
289	C₃×Q₈	—	2	4	no	—
290	C₃×D₄	—	2	4	no	—
291	C₃×D₄	—	4	4	no	—
292	C₂×C₃×C₄	—	2	2	no	—
293	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
294	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
295	#67	—	4	4	no	—
296	#67	—	4	8	no	—
297	C₂×Dic₃	—	2	2	no	—
298	C₂×Dic₃	C₂×C₅×D₄	1	1	yes	characteristic
299	C₂×Dic₃	C₂×C₅×D₄	1	2	yes	—
300	D₁₂	—	2	4	no	—
301	D₁₂	—	4	4	no	—
302	C₄×D₃	—	4	4	no	—
303	C₄×D₃	C₅×SD₁₆	1	8	yes	complemented
304	C₄×D₃	C₂×C₅×D₄	1	4	yes	—
305	Dic₆	—	2	4	no	—
306	Dic₆	—	4	4	no	—
307	C₃×C₈	C₂×C₅×D₄	1	4	yes	complemented
308	C₃⋊C₈	C₂×C₅×D₄	1	4	yes	complemented
309	C₂²×C₅	—	3	2	no	—
310	C₂²×C₅	—	3	4	no	—
311	C₂²×C₅	—	4	2	no	—
312	C₂²×C₅	—	4	4	no	—
313	C₂²×C₅	—	12	2	no	—
314	C₂²×C₅	—	12	4	no	—
315	C₂²×C₅	—	24	8	no	—
316	C₂²×C₅	C₂×D₃×D₄	1	1	yes	characteristic
317	C₄×C₅	—	3	2	no	—
318	C₄×C₅	—	3	4	no	—
319	C₄×C₅	—	4	2	no	—
320	C₄×C₅	—	12	2	no	—
321	C₄×C₅	D₃×SD₁₆	1	4	yes	complemented
322	C₄×C₅	C₂×D₃×D₄	1	2	yes	—
323	C₂⁴	—	6	2	no	—
324	C₂×Q₈	—	3	2	no	—
325	C₂×Q₈	—	6	2	no	—
326	C₂×Q₈	—	6	8	no	—
327	C₂×Q₈	C₂²×C₅×D₃	1	2	yes	—
328	C₂×D₄	—	2	2	no	—
329	C₂×D₄	—	3	2	no	—
330	C₂×D₄	—	6	8	no	—
331	C₂×D₄	—	6	4	no	—
332	C₂×D₄	—	6	2	no	—
333	C₂×D₄	—	6	2	no	—
334	C₂×D₄	—	12	8	no	—
335	C₂×D₄	C₂²×C₅×D₃	1	2	yes	—
336	C₂²×C₄	—	3	2	no	—
337	C₂²×C₄	—	3	1	no	—
338	C₂²×C₄	—	6	2	no	—
339	SD₁₆	—	2	8	no	—
340	SD₁₆	—	6	8	no	—
341	SD₁₆	—	6	8	no	—
342	SD₁₆	—	6	8	no	—
343	C₂×C₈	—	3	2	no	—
344	C₂×C₈	—	3	8	no	—
345	C₂×C₈	C₂²×C₅×D₃	1	2	yes	—
346	C₄⋊C₄	—	2	2	no	—
347	C₄⋊C₄	—	6	4	no	—
348	C₄⋊C₄	—	6	2	no	—
349	C₄²	—	3	2	no	—
350	C₄²	—	3	1	no	—
351	C₄²	C₂²×C₅×D₃	1	1	yes	characteristic
352	C₃×C₅	C₂×#492	1	1	yes	characteristic, complemented, Hall
353	C₂²×C₃	—	4	2	no	—
354	C₂²×C₃	—	4	4	no	—
355	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
356	C₂×D₃	—	4	2	no	—
357	C₂×D₃	—	4	4	no	—
358	C₂×D₃	—	8	8	no	—
359	C₂×D₃	C₅×#127	1	2	yes	—
360	C₂×D₃	C₂×C₅×SD₁₆	1	4	yes	—
361	C₃×C₄	—	4	2	no	—
362	C₃×C₄	C₂×C₅×SD₁₆	1	4	yes	complemented
363	C₃×C₄	C₂²×C₅×D₄	1	2	yes	—
364	Dic₃	—	4	2	no	—
365	Dic₃	C₅×#127	1	2	yes	—
366	Dic₃	C₂×C₅×SD₁₆	1	4	yes	complemented
367	C₂×C₅	—	3	4	no	—
368	C₂×C₅	—	8	2	no	—
369	C₂×C₅	—	24	2	no	—
370	C₂×C₅	D₃×#127	1	1	yes	characteristic
371	C₂×C₅	C₂×D₃×SD₁₆	1	2	yes	—
372	C₂³	—	2	2	no	—
373	C₂³	—	3	1	no	—
374	C₂³	—	6	2	no	—
375	C₂³	—	12	4	no	—
376	C₂³	—	12	8	no	—
377	Q₈	—	2	4	no	—
378	Q₈	—	6	4	no	—
379	Q₈	—	12	4	no	—
380	D₄	—	2	4	no	—
381	D₄	—	4	4	no	—
382	D₄	—	6	4	no	—
383	D₄	—	12	4	no	—
384	D₄	—	12	8	no	—
385	D₄	—	12	4	no	—
386	C₂×C₄	—	2	2	no	—
387	C₂×C₄	—	3	2	no	—
388	C₂×C₄	—	3	1	no	—
389	C₂×C₄	—	3	8	no	—
390	C₂×C₄	—	3	4	no	—
391	C₂×C₄	—	6	2	no	—
392	C₂×C₄	—	12	4	no	—
393	C₂×C₄	C₅×D₃×D₄	1	2	yes	—
394	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
395	C₈	—	3	4	no	—
396	C₈	C₅×D₃×D₄	1	4	yes	complemented
397	C₂×C₃	—	8	2	no	—
398	C₂×C₃	C₂×C₅×#127	1	1	yes	characteristic
399	C₂×C₃	C₂²×C₅×SD₁₆	1	2	yes	—
400	D₃	—	8	2	no	—
401	D₃	C₅×#492	1	4	yes	direct product factor
402	C₅	D₃×#492	1	1	yes	characteristic, direct product factor, Sylow
403	C₂²	—	3	2	no	—
404	C₂²	—	3	4	no	—
405	C₂²	—	4	2	no	—
406	C₂²	—	4	4	no	—
407	C₂²	—	12	2	no	—
408	C₂²	—	12	4	no	—
409	C₂²	—	24	8	no	—
410	C₂²	C₂×C₅×D₃×D₄	1	1	yes	characteristic
411	C₄	—	3	2	no	—
412	C₄	—	3	4	no	—
413	C₄	—	4	2	no	—
414	C₄	—	12	2	no	—
415	C₄	C₅×D₃×SD₁₆	1	4	yes	complemented
416	C₄	C₂×C₅×D₃×D₄	1	2	yes	—
417	C₃	C₂×C₅×#492	1	1	yes	characteristic, complemented, Sylow
418	C₂	—	3	4	no	—
419	C₂	—	8	2	no	—
420	C₂	—	24	2	no	—
421	C₂	C₅×D₃×#127	1	1	yes	characteristic
422	C₂	C₂×C₅×D₃×SD₁₆	1	2	yes	—

	subgroup	G/H
center	C₂²×C₅	C₂×D₃×D₄
commutator, cosocle	C₂×C₃×C₄	C₂⁴×C₅
Frattini	C₂×C₄	C₂³×C₅×D₃
Fitting	C₃×C₅×#492	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
prime radical	C₅×D₃×#127	C₂
hypercenter	C₅×#492	D₃
hypocenter	C₃	C₂×C₅×#492
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₄²×C₅ ◁ C₅×#492

Complements

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

N	H ≅ G/N	type
1. C₂×C₅×D₃×SD₁₆	C₂	semidirect
2. C₅×D₃×C₄⋊Q₈	C₂	semidirect
4. C₃×C₅×#492	C₂	semidirect
5. C₅×#5175	C₂	semidirect
6. C₅×#5085	C₂	semidirect
7. C₅×#5076	C₂	semidirect
8. C₅×#4693	C₂	semidirect
9. C₄×C₅×D₃×C₈	C₂	semidirect
14. C₂×C₃×C₅×SD₁₆	C₂²	semidirect
15. C₃×C₅×C₄⋊Q₈	C₂²	semidirect
17. C₅×#944	C₂²	semidirect
18. C₂×C₅×#215	C₂²	semidirect
21. C₂×C₅×#214	C₂²	semidirect
23. C₂×C₅×#204	C₂²	semidirect
29. C₅×#869	C₂²	semidirect
30. C₃×C₄×C₅×C₈	C₂²	semidirect
31. C₅×C₈×Dic₃	C₂²	semidirect
32. C₄×C₅×C₃⋊C₈	C₂²	semidirect
33. D₃×#492	C₅	direct (N × H)
41. C₅×#492	D₃	direct (N × H)
71. C₅×D₃×C₈	D₄	semidirect
72. C₂×D₃×SD₁₆	C₂×C₅	semidirect
73. D₃×C₄⋊Q₈	C₂×C₅	semidirect
75. C₃×#492	C₂×C₅	semidirect
76. #5175	C₂×C₅	semidirect
77. #5085	C₂×C₅	semidirect
78. #5076	C₂×C₅	semidirect
79. #4693	C₂×C₅	semidirect
80. C₄×D₃×C₈	C₂×C₅	semidirect
88. C₂×C₅×SD₁₆	C₂×D₃	semidirect
93. C₅×C₄⋊Q₈	C₂×D₃	semidirect
102. C₄×C₅×C₈	C₂×D₃	semidirect
123. C₄×C₅×D₃	SD₁₆	semidirect
127. C₃×C₅×C₈	C₂×D₄	semidirect
128. C₅×C₃⋊C₈	C₂×D₄	semidirect
132. C₂×C₃×SD₁₆	C₂²×C₅	semidirect
133. C₃×C₄⋊Q₈	C₂²×C₅	semidirect
135. #944	C₂²×C₅	semidirect
136. C₂×#215	C₂²×C₅	semidirect
139. C₂×#214	C₂²×C₅	semidirect
141. C₂×#204	C₂²×C₅	semidirect
147. #869	C₂²×C₅	semidirect
148. C₃×C₄×C₈	C₂²×C₅	semidirect
149. C₈×Dic₃	C₂²×C₅	semidirect
150. C₄×C₃⋊C₈	C₂²×C₅	semidirect
187. #492	C₅×D₃	direct (N × H)
198. C₃×C₄×C₅	C₂×SD₁₆	semidirect
202. C₅×Dic₃	C₂×SD₁₆	semidirect
231. D₃×C₈	C₅×D₄	semidirect
256. C₅×C₈	D₃×D₄	semidirect
264. C₂×SD₁₆	C₂×C₅×D₃	semidirect
269. C₄⋊Q₈	C₂×C₅×D₃	semidirect
278. C₄×C₈	C₂×C₅×D₃	semidirect
283. C₅×D₃	#492	direct (N × H)
303. C₄×D₃	C₅×SD₁₆	semidirect
307. C₃×C₈	C₂×C₅×D₄	semidirect
308. C₃⋊C₈	C₂×C₅×D₄	semidirect
321. C₄×C₅	D₃×SD₁₆	semidirect
352. C₃×C₅	C₂×#492	semidirect
362. C₃×C₄	C₂×C₅×SD₁₆	semidirect
366. Dic₃	C₂×C₅×SD₁₆	semidirect
396. C₈	C₅×D₃×D₄	semidirect
401. D₃	C₅×#492	direct (N × H)
402. C₅	D₃×#492	direct (N × H)
415. C₄	C₅×D₃×SD₁₆	semidirect
417. C₃	C₂×C₅×#492	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅×D₃×SD₁₆	2
C₅×D₃×C₄⋊Q₈	2
C₅×D₃×#127	2
C₃×C₅×#492	2
C₅×#5175	2
C₅×#5085	2
C₅×#5076	2
C₅×#4693	2
C₄×C₅×D₃×C₈	2
C₂×C₅×#492	3
D₃×#492	5

Subgroups — C5×D3×#492 #14438721

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×D₃×#492 #14438721