Subgroups — C₃×D₅×#492 #14438722

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×C₃×D₅×SD₁₆	C₂	1	4	yes	maximal, complemented
2	C₃×D₅×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×D₅×#127	C₂	1	1	yes	maximal, characteristic
4	C₃×C₅×#492	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#65464	C₂	1	4	yes	maximal, complemented
6	C₃×#65374	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#65365	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#64982	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×C₄×C₈×D₅	C₂	1	1	yes	maximal, characteristic, complemented
10	D₅×#492	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₂×C₃×Q₈×D₅	C₂²	1	2	yes	—
12	C₂×C₃×D₄×D₅	—	2	2	no	—
13	C₂×C₃×D₄×D₅	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	C₃×#4090	C₂²	1	2	yes	complemented
18	C₂×C₃×#688	C₂²	1	4	yes	complemented
19	C₃×#4086	—	2	2	no	—
20	C₃×#4086	C₂²	1	2	yes	—
21	C₂×C₃×#687	C₂²	1	4	yes	complemented
22	C₃×D₅×SD₁₆	—	2	16	no	—
23	C₂×C₃×#677	C₂²	1	4	yes	complemented
24	C₂×C₃×C₈×D₅	C₂²	1	2	yes	—
25	C₃×D₅×C₄⋊C₄	—	2	2	no	—
26	C₃×#4034	—	2	2	no	—
27	C₃×#4020	C₂²	1	1	yes	characteristic
28	C₃×C₄²×D₅	C₂²	1	1	yes	characteristic
29	C₃×#4015	C₂²	1	1	yes	characteristic, complemented
30	C₃×C₄×C₅×C₈	C₂²	1	1	yes	characteristic, complemented
31	C₃×C₈×Dic₅	C₂²	1	2	yes	complemented
32	C₃×C₄×#168	C₂²	1	1	yes	characteristic, complemented
33	C₂×C₃×#492	—	5	1	no	maximal, Hall
34	C₂×D₅×SD₁₆	C₂×C₃	1	4	yes	complemented
35	D₅×C₄⋊Q₈	C₂×C₃	1	1	yes	characteristic, complemented
36	D₅×#127	C₂×C₃	1	1	yes	characteristic
37	C₅×#492	C₂×C₃	1	1	yes	characteristic, complemented
38	#65464	C₂×C₃	1	4	yes	complemented
39	#65374	C₂×C₃	1	1	yes	characteristic, complemented
40	#65365	C₂×C₃	1	1	yes	characteristic, complemented
41	#64982	C₂×C₃	1	1	yes	characteristic, complemented
42	C₄×C₈×D₅	C₂×C₃	1	1	yes	characteristic, complemented
43	C₂³×C₃×D₅	—	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×C₃×C₂²⋊D₅	—	2	2	no	—
48	C₂×C₃×C₂²⋊D₅	—	2	4	no	—
49	C₃×Q₈×D₅	—	2	8	no	—
50	C₃×D₄×D₅	—	2	8	no	—
51	C₃×D₄×D₅	—	4	8	no	—
52	C₂×C₃×D₂₀	—	2	2	no	—
53	C₂×C₃×D₂₀	C₂³	1	2	yes	—
54	C₂×C₃×C₄×D₅	—	2	2	no	—
55	C₂×C₃×C₄×D₅	D₄	1	2	yes	—
56	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
57	C₂×C₃×Dic₁₀	—	2	2	no	—
58	C₂×C₃×Dic₁₀	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	C₃×#688	—	2	8	no	—
64	C₃×#687	—	2	8	no	—
65	C₃×C₄⋊Dic₅	—	2	2	no	—
66	C₃×#683	—	2	4	no	—
67	C₃×C₄×Dic₅	D₄	1	2	yes	—
68	C₃×C₄×Dic₅	C₂³	1	1	yes	characteristic
69	C₂×C₃×#168	C₂³	1	2	yes	—
70	C₃×#677	—	2	8	no	—
71	C₃×C₈×D₅	D₄	1	8	yes	complemented
72	C₂²×C₃×SD₁₆	—	5	4	no	—
73	C₂×C₃×C₄⋊Q₈	—	5	1	no	—
74	C₂×C₃×#127	—	5	1	no	—
75	C₃×#492	—	5	4	no	—
76	C₃×#492	—	5	1	no	—
77	C₃×#492	—	5	1	no	—
78	C₃×#492	—	5	1	no	—
79	C₃×#492	D₅	1	1	yes	characteristic, direct product factor
80	C₂×C₃×C₄×C₈	—	5	1	no	—
81	C₂×Q₈×D₅	C₂²×C₃	1	2	yes	—
82	C₂×D₄×D₅	—	2	2	no	—
83	C₂×D₄×D₅	C₂²×C₃	1	2	yes	—
84	C₂×C₅×SD₁₆	C₂²×C₃	1	4	yes	complemented
85	C₅×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
86	C₅×#127	C₂²×C₃	1	1	yes	characteristic
87	#4090	C₂²×C₃	1	2	yes	complemented
88	C₂×#688	C₂²×C₃	1	4	yes	complemented
89	#4086	—	2	2	no	—
90	#4086	C₂²×C₃	1	2	yes	—
91	C₂×#687	C₂²×C₃	1	4	yes	complemented
92	D₅×SD₁₆	—	2	16	no	—
93	C₂×#677	C₂²×C₃	1	4	yes	complemented
94	C₂×C₈×D₅	C₂²×C₃	1	2	yes	—
95	D₅×C₄⋊C₄	—	2	2	no	—
96	#4034	—	2	2	no	—
97	#4020	C₂²×C₃	1	1	yes	characteristic
98	C₄²×D₅	C₂²×C₃	1	1	yes	characteristic
99	#4015	C₂²×C₃	1	1	yes	characteristic, complemented
100	C₄×C₅×C₈	C₂²×C₃	1	1	yes	characteristic, complemented
101	C₈×Dic₅	C₂²×C₃	1	2	yes	complemented
102	C₄×#168	C₂²×C₃	1	1	yes	characteristic, complemented
103	C₂×#492	—	5	1	no	Sylow
104	C₂³×C₃×C₅	—	2	2	no	—
105	C₂²×C₃×D₅	—	2	2	no	—
106	C₂²×C₃×D₅	—	4	4	no	—
107	C₂²×C₃×D₅	—	4	8	no	—
108	C₂²×C₃×D₅	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	C₃×C₂²⋊D₅	—	4	4	no	—
116	C₃×C₂²⋊D₅	—	4	8	no	—
117	C₂×C₃×Dic₅	—	2	2	no	—
118	C₂×C₃×Dic₅	C₂×D₄	1	1	yes	characteristic
119	C₂×C₃×Dic₅	C₂×D₄	1	2	yes	—
120	C₃×D₂₀	—	2	4	no	—
121	C₃×D₂₀	—	4	4	no	—
122	C₃×C₄×D₅	—	4	4	no	—
123	C₃×C₄×D₅	SD₁₆	1	8	yes	complemented
124	C₃×C₄×D₅	C₂×D₄	1	4	yes	—
125	C₃×Dic₁₀	—	2	4	no	—
126	C₃×Dic₁₀	—	4	4	no	—
127	C₃×C₅×C₈	C₂×D₄	1	4	yes	complemented
128	C₃×#168	C₂×D₄	1	4	yes	complemented
129	C₂²×C₃×Q₈	—	5	2	no	—
130	C₂²×C₃×D₄	—	5	2	no	—
131	C₂²×C₃×D₄	—	10	2	no	—
132	C₂×C₃×SD₁₆	—	5	4	no	—
133	C₂×C₃×SD₁₆	—	5	4	no	—
134	C₂×C₃×SD₁₆	—	5	4	no	—
135	C₂×C₃×SD₁₆	—	10	16	no	—
136	C₂×C₃×SD₁₆	C₂×D₅	1	4	yes	complemented
137	C₂²×C₃×C₈	—	5	2	no	—
138	C₃×C₄⋊Q₈	—	5	2	no	—
139	C₃×C₄⋊Q₈	—	5	1	no	—
140	C₃×C₄⋊Q₈	—	10	2	no	—
141	C₃×C₄⋊Q₈	C₂×D₅	1	1	yes	characteristic, complemented
142	C₃×#127	—	5	2	no	—
143	C₃×#127	—	5	1	no	—
144	C₃×#127	—	10	2	no	—
145	C₃×#127	C₂×D₅	1	1	yes	characteristic
146	C₂×C₃×C₄⋊C₄	—	10	2	no	—
147	C₂×C₃×C₄²	—	5	1	no	—
148	C₃×C₄×C₈	—	5	2	no	—
149	C₃×C₄×C₈	—	5	1	no	—
150	C₃×C₄×C₈	C₂×D₅	1	1	yes	characteristic, complemented
151	C₂³×D₅	—	2	2	no	—
152	C₂×C₅×Q₈	C₂³×C₃	1	2	yes	—
153	C₂×C₅×D₄	—	2	2	no	—
154	C₂×C₅×D₄	C₂³×C₃	1	2	yes	—
155	C₂×C₂²⋊D₅	—	2	4	no	—
156	C₂×C₂²⋊D₅	—	2	2	no	—
157	Q₈×D₅	—	2	8	no	—
158	D₄×D₅	—	2	8	no	—
159	D₄×D₅	—	4	8	no	—
160	C₂×D₂₀	—	2	2	no	—
161	C₂×D₂₀	C₂³×C₃	1	2	yes	—
162	C₂×C₄×D₅	—	2	2	no	—
163	C₂×C₄×D₅	C₃×D₄	1	2	yes	—
164	C₂×C₄×D₅	C₂³×C₃	1	1	yes	characteristic
165	C₂×Dic₁₀	—	2	2	no	—
166	C₂×Dic₁₀	C₂³×C₃	1	2	yes	—
167	C₅×SD₁₆	—	2	8	no	—
168	C₂×C₅×C₈	C₂³×C₃	1	2	yes	—
169	C₅×C₄⋊C₄	—	2	2	no	—
170	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
171	#688	—	2	8	no	—
172	#687	—	2	8	no	—
173	C₄⋊Dic₅	—	2	2	no	—
174	#683	—	2	4	no	—
175	C₄×Dic₅	C₃×D₄	1	2	yes	—
176	C₄×Dic₅	C₂³×C₃	1	1	yes	characteristic
177	C₂×#168	C₂³×C₃	1	2	yes	—
178	#677	—	2	8	no	—
179	C₈×D₅	C₃×D₄	1	8	yes	complemented
180	C₂²×SD₁₆	—	5	4	no	—
181	C₂×C₄⋊Q₈	—	5	1	no	—
182	C₂×#127	—	5	1	no	—
183	#492	—	5	4	no	—
184	#492	—	5	1	no	—
185	#492	—	5	1	no	—
186	#492	—	5	1	no	—
187	#492	C₃×D₅	1	1	yes	characteristic, direct product factor
188	C₂×C₄×C₈	—	5	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×C₃×D₅	—	4	2	no	—
193	C₂×C₃×D₅	—	4	4	no	—
194	C₂×C₃×D₅	—	8	8	no	—
195	C₂×C₃×D₅	#127	1	2	yes	—
196	C₂×C₃×D₅	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	C₃×Dic₅	—	4	2	no	—
201	C₃×Dic₅	#127	1	2	yes	—
202	C₃×Dic₅	C₂×SD₁₆	1	4	yes	complemented
203	C₂⁴×C₃	—	10	2	no	—
204	C₂×C₃×Q₈	—	5	2	no	—
205	C₂×C₃×Q₈	—	10	2	no	—
206	C₂×C₃×Q₈	—	10	8	no	—
207	C₂×C₃×Q₈	C₂²×D₅	1	2	yes	—
208	C₂×C₃×D₄	—	2	2	no	—
209	C₂×C₃×D₄	—	5	2	no	—
210	C₂×C₃×D₄	—	10	8	no	—
211	C₂×C₃×D₄	—	10	4	no	—
212	C₂×C₃×D₄	—	10	2	no	—
213	C₂×C₃×D₄	—	10	2	no	—
214	C₂×C₃×D₄	—	20	8	no	—
215	C₂×C₃×D₄	C₂²×D₅	1	2	yes	—
216	C₂²×C₃×C₄	—	5	2	no	—
217	C₂²×C₃×C₄	—	5	1	no	—
218	C₂²×C₃×C₄	—	10	2	no	—
219	C₃×SD₁₆	—	2	8	no	—
220	C₃×SD₁₆	—	10	8	no	—
221	C₃×SD₁₆	—	10	8	no	—
222	C₃×SD₁₆	—	10	8	no	—
223	C₂×C₃×C₈	—	5	2	no	—
224	C₂×C₃×C₈	—	5	8	no	—
225	C₂×C₃×C₈	C₂²×D₅	1	2	yes	—
226	C₃×C₄⋊C₄	—	2	2	no	—
227	C₃×C₄⋊C₄	—	10	4	no	—
228	C₃×C₄⋊C₄	—	10	2	no	—
229	C₃×C₄²	—	5	2	no	—
230	C₃×C₄²	—	5	1	no	—
231	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
232	C₂³×C₅	—	2	2	no	—
233	C₂²×D₅	—	2	2	no	—
234	C₂²×D₅	—	4	4	no	—
235	C₂²×D₅	—	4	8	no	—
236	C₂²×D₅	C₂×C₃×D₄	1	1	yes	characteristic
237	C₅×Q₈	—	2	4	no	—
238	C₅×D₄	—	2	4	no	—
239	C₅×D₄	—	4	4	no	—
240	C₂×C₄×C₅	—	2	2	no	—
241	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
242	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
243	C₂²⋊D₅	—	4	4	no	—
244	C₂²⋊D₅	—	4	8	no	—
245	C₂×Dic₅	—	2	2	no	—
246	C₂×Dic₅	C₂×C₃×D₄	1	1	yes	characteristic
247	C₂×Dic₅	C₂×C₃×D₄	1	2	yes	—
248	D₂₀	—	2	4	no	—
249	D₂₀	—	4	4	no	—
250	C₄×D₅	—	4	4	no	—
251	C₄×D₅	C₃×SD₁₆	1	8	yes	complemented
252	C₄×D₅	C₂×C₃×D₄	1	4	yes	—
253	Dic₁₀	—	2	4	no	—
254	Dic₁₀	—	4	4	no	—
255	C₅×C₈	C₂×C₃×D₄	1	4	yes	complemented
256	#168	C₂×C₃×D₄	1	4	yes	complemented
257	C₂²×Q₈	—	5	2	no	—
258	C₂²×D₄	—	5	2	no	—
259	C₂²×D₄	—	10	2	no	—
260	C₂×SD₁₆	—	5	4	no	—
261	C₂×SD₁₆	—	5	4	no	—
262	C₂×SD₁₆	—	5	4	no	—
263	C₂×SD₁₆	—	10	16	no	—
264	C₂×SD₁₆	C₂×C₃×D₅	1	4	yes	complemented
265	C₂²×C₈	—	5	2	no	—
266	C₄⋊Q₈	—	5	2	no	—
267	C₄⋊Q₈	—	5	1	no	—
268	C₄⋊Q₈	—	10	2	no	—
269	C₄⋊Q₈	C₂×C₃×D₅	1	1	yes	characteristic, complemented
270	#127	—	5	2	no	—
271	#127	—	5	1	no	—
272	#127	—	10	2	no	—
273	#127	C₂×C₃×D₅	1	1	yes	characteristic
274	C₂×C₄⋊C₄	—	10	2	no	—
275	C₂×C₄²	—	5	1	no	—
276	C₄×C₈	—	5	2	no	—
277	C₄×C₈	—	5	1	no	—
278	C₄×C₈	C₂×C₃×D₅	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	C₃×D₅	—	8	2	no	—
283	C₃×D₅	#492	1	4	yes	direct product factor
284	C₂³×C₃	—	2	2	no	—
285	C₂³×C₃	—	5	1	no	—
286	C₂³×C₃	—	10	2	no	—
287	C₂³×C₃	—	20	4	no	—
288	C₂³×C₃	—	20	8	no	—
289	C₃×Q₈	—	2	4	no	—
290	C₃×Q₈	—	10	4	no	—
291	C₃×Q₈	—	20	4	no	—
292	C₃×D₄	—	2	4	no	—
293	C₃×D₄	—	4	4	no	—
294	C₃×D₄	—	10	4	no	—
295	C₃×D₄	—	20	4	no	—
296	C₃×D₄	—	20	8	no	—
297	C₃×D₄	—	20	4	no	—
298	C₂×C₃×C₄	—	2	2	no	—
299	C₂×C₃×C₄	—	5	2	no	—
300	C₂×C₃×C₄	—	5	1	no	—
301	C₂×C₃×C₄	—	5	4	no	—
302	C₂×C₃×C₄	—	5	8	no	—
303	C₂×C₃×C₄	—	10	2	no	—
304	C₂×C₃×C₄	—	20	4	no	—
305	C₂×C₃×C₄	D₄×D₅	1	2	yes	—
306	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
307	C₃×C₈	—	5	4	no	—
308	C₃×C₈	D₄×D₅	1	4	yes	complemented
309	C₂²×C₅	—	4	4	no	—
310	C₂²×C₅	—	4	2	no	—
311	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
312	C₂×D₅	—	4	4	no	—
313	C₂×D₅	—	4	2	no	—
314	C₂×D₅	—	8	8	no	—
315	C₂×D₅	C₃×#127	1	2	yes	—
316	C₂×D₅	C₂×C₃×SD₁₆	1	4	yes	—
317	C₄×C₅	—	4	2	no	—
318	C₄×C₅	C₂×C₃×SD₁₆	1	4	yes	complemented
319	C₄×C₅	C₂²×C₃×D₄	1	2	yes	—
320	Dic₅	—	4	2	no	—
321	Dic₅	C₃×#127	1	2	yes	—
322	Dic₅	C₂×C₃×SD₁₆	1	4	yes	complemented
323	C₂⁴	—	10	2	no	—
324	C₂×Q₈	—	5	2	no	—
325	C₂×Q₈	—	10	2	no	—
326	C₂×Q₈	—	10	8	no	—
327	C₂×Q₈	C₂²×C₃×D₅	1	2	yes	—
328	C₂×D₄	—	2	2	no	—
329	C₂×D₄	—	5	2	no	—
330	C₂×D₄	—	10	8	no	—
331	C₂×D₄	—	10	4	no	—
332	C₂×D₄	—	10	2	no	—
333	C₂×D₄	—	10	2	no	—
334	C₂×D₄	—	20	8	no	—
335	C₂×D₄	C₂²×C₃×D₅	1	2	yes	—
336	C₂²×C₄	—	5	2	no	—
337	C₂²×C₄	—	5	1	no	—
338	C₂²×C₄	—	10	2	no	—
339	SD₁₆	—	2	8	no	—
340	SD₁₆	—	10	8	no	—
341	SD₁₆	—	10	8	no	—
342	SD₁₆	—	10	8	no	—
343	C₂×C₈	—	5	2	no	—
344	C₂×C₈	—	5	8	no	—
345	C₂×C₈	C₂²×C₃×D₅	1	2	yes	—
346	C₄⋊C₄	—	2	2	no	—
347	C₄⋊C₄	—	10	4	no	—
348	C₄⋊C₄	—	10	2	no	—
349	C₄²	—	5	2	no	—
350	C₄²	—	5	1	no	—
351	C₄²	C₂²×C₃×D₅	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	—	5	2	no	—
356	C₂²×C₃	—	5	4	no	—
357	C₂²×C₃	—	20	2	no	—
358	C₂²×C₃	—	20	4	no	—
359	C₂²×C₃	—	40	8	no	—
360	C₂²×C₃	C₂×D₄×D₅	1	1	yes	characteristic
361	C₃×C₄	—	4	2	no	—
362	C₃×C₄	—	5	2	no	—
363	C₃×C₄	—	5	4	no	—
364	C₃×C₄	—	20	2	no	—
365	C₃×C₄	D₅×SD₁₆	1	4	yes	complemented
366	C₃×C₄	C₂×D₄×D₅	1	2	yes	—
367	C₂×C₅	—	8	2	no	—
368	C₂×C₅	C₂×C₃×#127	1	1	yes	characteristic
369	C₂×C₅	C₂²×C₃×SD₁₆	1	2	yes	—
370	D₅	—	8	2	no	—
371	D₅	C₃×#492	1	4	yes	direct product factor
372	C₂³	—	2	2	no	—
373	C₂³	—	5	1	no	—
374	C₂³	—	10	2	no	—
375	C₂³	—	20	4	no	—
376	C₂³	—	20	8	no	—
377	Q₈	—	2	4	no	—
378	Q₈	—	10	4	no	—
379	Q₈	—	20	4	no	—
380	D₄	—	2	4	no	—
381	D₄	—	4	4	no	—
382	D₄	—	10	4	no	—
383	D₄	—	20	4	no	—
384	D₄	—	20	8	no	—
385	D₄	—	20	4	no	—
386	C₂×C₄	—	2	2	no	—
387	C₂×C₄	—	5	2	no	—
388	C₂×C₄	—	5	1	no	—
389	C₂×C₄	—	5	4	no	—
390	C₂×C₄	—	5	8	no	—
391	C₂×C₄	—	10	2	no	—
392	C₂×C₄	—	20	4	no	—
393	C₂×C₄	C₃×D₄×D₅	1	2	yes	—
394	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
395	C₈	—	5	4	no	—
396	C₈	C₃×D₄×D₅	1	4	yes	complemented
397	C₂×C₃	—	5	4	no	—
398	C₂×C₃	—	8	2	no	—
399	C₂×C₃	—	40	2	no	—
400	C₂×C₃	D₅×#127	1	1	yes	characteristic
401	C₂×C₃	C₂×D₅×SD₁₆	1	2	yes	—
402	C₅	C₂×C₃×#492	1	1	yes	characteristic, complemented, Sylow
403	C₂²	—	4	2	no	—
404	C₂²	—	4	4	no	—
405	C₂²	—	5	2	no	—
406	C₂²	—	5	4	no	—
407	C₂²	—	20	2	no	—
408	C₂²	—	20	4	no	—
409	C₂²	—	40	8	no	—
410	C₂²	C₂×C₃×D₄×D₅	1	1	yes	characteristic
411	C₄	—	4	2	no	—
412	C₄	—	5	2	no	—
413	C₄	—	5	4	no	—
414	C₄	—	20	2	no	—
415	C₄	C₃×D₅×SD₁₆	1	4	yes	complemented
416	C₄	C₂×C₃×D₄×D₅	1	2	yes	—
417	C₃	D₅×#492	1	1	yes	characteristic, direct product factor, Sylow
418	C₂	—	5	4	no	—
419	C₂	—	8	2	no	—
420	C₂	—	40	2	no	—
421	C₂	C₃×D₅×#127	1	1	yes	characteristic
422	C₂	C₂×C₃×D₅×SD₁₆	1	2	yes	—

	subgroup	G/H
center	C₂²×C₃	C₂×D₄×D₅
commutator, cosocle	C₂×C₄×C₅	C₂⁴×C₃
Frattini	C₂×C₄	C₂³×C₃×D₅
Fitting	C₃×C₅×#492	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
prime radical	C₃×D₅×#127	C₂
hypercenter	C₃×#492	D₅
hypocenter	C₅	C₂×C₃×#492
LCS	G ▷ C₂×C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×C₄² ◁ C₃×#492

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×D₅×SD₁₆	C₂	semidirect
2. C₃×D₅×C₄⋊Q₈	C₂	semidirect
4. C₃×C₅×#492	C₂	semidirect
5. C₃×#65464	C₂	semidirect
6. C₃×#65374	C₂	semidirect
7. C₃×#65365	C₂	semidirect
8. C₃×#64982	C₂	semidirect
9. C₃×C₄×C₈×D₅	C₂	semidirect
10. D₅×#492	C₃	direct (N × H)
14. C₂×C₃×C₅×SD₁₆	C₂²	semidirect
15. C₃×C₅×C₄⋊Q₈	C₂²	semidirect
17. C₃×#4090	C₂²	semidirect
18. C₂×C₃×#688	C₂²	semidirect
21. C₂×C₃×#687	C₂²	semidirect
23. C₂×C₃×#677	C₂²	semidirect
29. C₃×#4015	C₂²	semidirect
30. C₃×C₄×C₅×C₈	C₂²	semidirect
31. C₃×C₈×Dic₅	C₂²	semidirect
32. C₃×C₄×#168	C₂²	semidirect
34. C₂×D₅×SD₁₆	C₂×C₃	semidirect
35. D₅×C₄⋊Q₈	C₂×C₃	semidirect
37. C₅×#492	C₂×C₃	semidirect
38. #65464	C₂×C₃	semidirect
39. #65374	C₂×C₃	semidirect
40. #65365	C₂×C₃	semidirect
41. #64982	C₂×C₃	semidirect
42. C₄×C₈×D₅	C₂×C₃	semidirect
71. C₃×C₈×D₅	D₄	semidirect
79. C₃×#492	D₅	direct (N × H)
84. C₂×C₅×SD₁₆	C₂²×C₃	semidirect
85. C₅×C₄⋊Q₈	C₂²×C₃	semidirect
87. #4090	C₂²×C₃	semidirect
88. C₂×#688	C₂²×C₃	semidirect
91. C₂×#687	C₂²×C₃	semidirect
93. C₂×#677	C₂²×C₃	semidirect
99. #4015	C₂²×C₃	semidirect
100. C₄×C₅×C₈	C₂²×C₃	semidirect
101. C₈×Dic₅	C₂²×C₃	semidirect
102. C₄×#168	C₂²×C₃	semidirect
123. C₃×C₄×D₅	SD₁₆	semidirect
127. C₃×C₅×C₈	C₂×D₄	semidirect
128. C₃×#168	C₂×D₄	semidirect
136. C₂×C₃×SD₁₆	C₂×D₅	semidirect
141. C₃×C₄⋊Q₈	C₂×D₅	semidirect
150. C₃×C₄×C₈	C₂×D₅	semidirect
179. C₈×D₅	C₃×D₄	semidirect
187. #492	C₃×D₅	direct (N × H)
198. C₃×C₄×C₅	C₂×SD₁₆	semidirect
202. C₃×Dic₅	C₂×SD₁₆	semidirect
251. C₄×D₅	C₃×SD₁₆	semidirect
255. C₅×C₈	C₂×C₃×D₄	semidirect
256. #168	C₂×C₃×D₄	semidirect
264. C₂×SD₁₆	C₂×C₃×D₅	semidirect
269. C₄⋊Q₈	C₂×C₃×D₅	semidirect
278. C₄×C₈	C₂×C₃×D₅	semidirect
283. C₃×D₅	#492	direct (N × H)
308. C₃×C₈	D₄×D₅	semidirect
318. C₄×C₅	C₂×C₃×SD₁₆	semidirect
322. Dic₅	C₂×C₃×SD₁₆	semidirect
352. C₃×C₅	C₂×#492	semidirect
365. C₃×C₄	D₅×SD₁₆	semidirect
371. D₅	C₃×#492	direct (N × H)
396. C₈	C₃×D₄×D₅	semidirect
402. C₅	C₂×C₃×#492	semidirect
415. C₄	C₃×D₅×SD₁₆	semidirect
417. C₃	D₅×#492	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×SD₁₆	2
C₃×D₅×C₄⋊Q₈	2
C₃×D₅×#127	2
C₃×C₅×#492	2
C₃×#65464	2
C₃×#65374	2
C₃×#65365	2
C₃×#64982	2
C₃×C₄×C₈×D₅	2
D₅×#492	3
C₂×C₃×#492	5

Subgroups — C3×D5×#492 #14438722

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×D₅×#492 #14438722