Subgroups — C₂×C₃×#65464 #14438725

Order 1920.

1312 conjugacy classes of subgroups.

The subgroup lattice has 476 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×C₅×SD₁₆	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃×#4090	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₃×#688	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₃×#4086	C₂	1	1	yes	maximal, characteristic
5	C₂²×C₃×#687	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×C₃×#677	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#65464	C₂	1	8	yes	maximal, direct product factor
8	C₂×C₃×C₈×Dic₅	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#65464	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₂²×C₃×C₅×Q₈	C₂²	1	1	yes	characteristic
11	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
12	C₂²×C₃×C₂²⋊D₅	—	2	2	no	—
13	C₂²×C₃×D₂₀	C₂²	1	1	yes	characteristic
14	C₂²×C₃×Dic₁₀	C₂²	1	1	yes	characteristic
15	C₂×C₃×C₅×SD₁₆	—	2	4	no	—
16	C₂×C₃×C₅×SD₁₆	C₂²	1	4	yes	complemented
17	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
18	C₃×#4090	—	2	2	no	—
19	C₃×#4090	C₂²	1	4	yes	complemented
20	C₂×C₃×#688	—	2	4	no	—
21	C₂×C₃×#688	C₂²	1	4	yes	complemented
22	C₃×#4086	—	2	2	no	—
23	C₃×#4086	C₂²	1	4	yes	—
24	C₂×C₃×#687	—	2	4	no	—
25	C₂×C₃×#687	C₂²	1	4	yes	complemented
26	C₂×C₃×#683	—	2	2	no	—
27	C₂×C₃×C₄×Dic₅	C₂²	1	1	yes	characteristic
28	C₂²×C₃×#168	C₂²	1	1	yes	characteristic
29	C₂×C₃×#677	—	2	4	no	—
30	C₂×C₃×#677	C₂²	1	4	yes	complemented
31	C₃×C₈×Dic₅	C₂²	1	4	yes	complemented
32	C₂×C₃×#492	—	5	1	no	maximal, Hall
33	C₂²×C₅×SD₁₆	C₂×C₃	1	1	yes	characteristic, complemented
34	C₂×#4090	C₂×C₃	1	1	yes	characteristic, complemented
35	C₂²×#688	C₂×C₃	1	1	yes	characteristic, complemented
36	C₂×#4086	C₂×C₃	1	1	yes	characteristic
37	C₂²×#687	C₂×C₃	1	1	yes	characteristic, complemented
38	C₂²×#677	C₂×C₃	1	1	yes	characteristic, complemented
39	#65464	C₂×C₃	1	8	yes	direct product factor
40	C₂×C₈×Dic₅	C₂×C₃	1	1	yes	characteristic, complemented
41	C₂⁴×C₃×C₅	—	2	1	no	—
42	C₂³×C₃×D₅	—	2	1	no	—
43	C₂×C₃×C₅×Q₈	—	2	1	no	—
44	C₂×C₃×C₅×Q₈	—	2	2	no	—
45	C₂×C₃×C₅×Q₈	—	2	2	no	—
46	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
47	C₂×C₃×C₅×D₄	—	2	2	no	—
48	C₂×C₃×C₅×D₄	—	2	2	no	—
49	C₂×C₃×C₅×D₄	—	2	1	no	—
50	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
51	C₂²×C₃×C₄×C₅	—	2	1	no	—
52	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
53	C₂×C₃×C₂²⋊D₅	—	2	8	no	—
54	C₂×C₃×C₂²⋊D₅	—	4	8	no	—
55	C₂²×C₃×Dic₅	—	2	1	no	—
56	C₂²×C₃×Dic₅	D₄	1	2	yes	—
57	C₂×C₃×D₂₀	—	2	2	no	—
58	C₂×C₃×D₂₀	—	2	2	no	—
59	C₂×C₃×D₂₀	—	2	1	no	—
60	C₂×C₃×D₂₀	C₂³	1	2	yes	—
61	C₂×C₃×Dic₁₀	—	2	2	no	—
62	C₂×C₃×Dic₁₀	—	2	2	no	—
63	C₂×C₃×Dic₁₀	—	2	1	no	—
64	C₂×C₃×Dic₁₀	C₂³	1	2	yes	—
65	C₃×C₅×SD₁₆	—	2	8	no	—
66	C₂×C₃×C₅×C₈	D₄	1	4	yes	complemented
67	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
68	C₃×#688	—	2	8	no	—
69	C₃×#687	—	2	8	no	—
70	C₃×#683	—	2	8	no	—
71	C₃×C₄×Dic₅	D₄	1	2	yes	—
72	C₃×C₄×Dic₅	C₂³	1	2	yes	—
73	C₂×C₃×#168	D₄	1	4	yes	complemented
74	C₂×C₃×#168	C₂³	1	2	yes	—
75	C₃×#677	—	2	8	no	—
76	C₂²×C₃×SD₁₆	—	5	1	no	—
77	C₂²×C₃×SD₁₆	—	5	1	no	—
78	C₂²×C₃×SD₁₆	—	5	1	no	—
79	C₂²×C₃×SD₁₆	D₅	1	1	yes	characteristic, complemented
80	C₂×C₃×C₄⋊Q₈	—	5	1	no	—
81	C₂×C₃×#127	—	5	1	no	—
82	C₃×#492	—	5	8	no	—
83	C₂×C₃×C₄×C₈	—	5	1	no	—
84	C₂²×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic
85	C₂²×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
86	C₂²×C₂²⋊D₅	—	2	2	no	—
87	C₂²×D₂₀	C₂²×C₃	1	1	yes	characteristic
88	C₂²×Dic₁₀	C₂²×C₃	1	1	yes	characteristic
89	C₂×C₅×SD₁₆	—	2	4	no	—
90	C₂×C₅×SD₁₆	C₂²×C₃	1	4	yes	complemented
91	C₂²×C₅×C₈	C₂²×C₃	1	1	yes	characteristic
92	#4090	—	2	2	no	—
93	#4090	C₂²×C₃	1	4	yes	complemented
94	C₂×#688	—	2	4	no	—
95	C₂×#688	C₂²×C₃	1	4	yes	complemented
96	#4086	—	2	2	no	—
97	#4086	C₂²×C₃	1	4	yes	—
98	C₂×#687	—	2	4	no	—
99	C₂×#687	C₂²×C₃	1	4	yes	complemented
100	C₂×#683	—	2	2	no	—
101	C₂×C₄×Dic₅	C₂²×C₃	1	1	yes	characteristic
102	C₂²×#168	C₂²×C₃	1	1	yes	characteristic
103	C₂×#677	—	2	4	no	—
104	C₂×#677	C₂²×C₃	1	4	yes	complemented
105	C₈×Dic₅	C₂²×C₃	1	4	yes	complemented
106	C₂×#492	—	5	1	no	Sylow
107	C₂³×C₃×C₅	—	2	2	no	—
108	C₂³×C₃×C₅	—	4	2	no	—
109	C₂³×C₃×C₅	—	4	4	no	—
110	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
111	C₂²×C₃×D₅	—	2	2	no	—
112	C₂²×C₃×D₅	—	4	2	no	—
113	C₂²×C₃×D₅	—	4	4	no	—
114	C₃×C₅×Q₈	—	2	2	no	—
115	C₃×C₅×Q₈	—	2	2	no	—
116	C₃×C₅×Q₈	—	4	2	no	—
117	C₃×C₅×D₄	—	2	2	no	—
118	C₃×C₅×D₄	—	2	2	no	—
119	C₃×C₅×D₄	—	4	2	no	—
120	C₂×C₃×C₄×C₅	—	2	2	no	—
121	C₂×C₃×C₄×C₅	—	4	2	no	—
122	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
123	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
124	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
125	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
126	C₃×C₂²⋊D₅	—	4	16	no	—
127	C₂×C₃×Dic₅	—	2	2	no	—
128	C₂×C₃×Dic₅	—	4	2	no	—
129	C₂×C₃×Dic₅	SD₁₆	1	8	yes	complemented
130	C₂×C₃×Dic₅	C₂×D₄	1	4	yes	—
131	C₃×D₂₀	—	2	2	no	—
132	C₃×D₂₀	—	2	2	no	—
133	C₃×D₂₀	—	4	2	no	—
134	C₃×Dic₁₀	—	2	2	no	—
135	C₃×Dic₁₀	—	2	2	no	—
136	C₃×Dic₁₀	—	4	2	no	—
137	C₃×C₅×C₈	C₂×D₄	1	4	yes	complemented
138	C₃×#168	C₂×D₄	1	4	yes	complemented
139	C₂²×C₃×Q₈	—	5	1	no	—
140	C₂²×C₃×Q₈	C₂×D₅	1	1	yes	characteristic
141	C₂²×C₃×D₄	—	5	1	no	—
142	C₂²×C₃×D₄	—	10	2	no	—
143	C₂²×C₃×D₄	C₂×D₅	1	1	yes	characteristic
144	C₂×C₃×SD₁₆	—	2	4	no	—
145	C₂×C₃×SD₁₆	—	5	4	no	—
146	C₂×C₃×SD₁₆	—	5	4	no	—
147	C₂×C₃×SD₁₆	—	5	4	no	—
148	C₂×C₃×SD₁₆	—	10	4	no	—
149	C₂×C₃×SD₁₆	—	10	4	no	—
150	C₂×C₃×SD₁₆	—	10	4	no	—
151	C₂×C₃×SD₁₆	C₂×D₅	1	4	yes	complemented
152	C₂²×C₃×C₈	—	5	1	no	—
153	C₂²×C₃×C₈	C₂×D₅	1	1	yes	characteristic
154	C₃×C₄⋊Q₈	—	5	4	no	—
155	C₃×C₄⋊Q₈	—	10	2	no	—
156	C₃×#127	—	5	4	no	—
157	C₃×#127	—	10	2	no	—
158	C₂×C₃×C₄⋊C₄	—	10	2	no	—
159	C₂×C₃×C₄²	—	5	1	no	—
160	C₃×C₄×C₈	—	5	4	no	—
161	C₂⁴×C₅	—	2	1	no	—
162	C₂³×D₅	—	2	1	no	—
163	C₂×C₅×Q₈	—	2	1	no	—
164	C₂×C₅×Q₈	—	2	2	no	—
165	C₂×C₅×Q₈	—	2	2	no	—
166	C₂×C₅×Q₈	C₂³×C₃	1	2	yes	—
167	C₂×C₅×D₄	—	2	2	no	—
168	C₂×C₅×D₄	—	2	2	no	—
169	C₂×C₅×D₄	—	2	1	no	—
170	C₂×C₅×D₄	C₂³×C₃	1	2	yes	—
171	C₂²×C₄×C₅	—	2	1	no	—
172	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
173	C₂×C₂²⋊D₅	—	2	8	no	—
174	C₂×C₂²⋊D₅	—	4	8	no	—
175	C₂²×Dic₅	—	2	1	no	—
176	C₂²×Dic₅	C₃×D₄	1	2	yes	—
177	C₂×D₂₀	—	2	2	no	—
178	C₂×D₂₀	—	2	2	no	—
179	C₂×D₂₀	—	2	1	no	—
180	C₂×D₂₀	C₂³×C₃	1	2	yes	—
181	C₂×Dic₁₀	—	2	2	no	—
182	C₂×Dic₁₀	—	2	2	no	—
183	C₂×Dic₁₀	—	2	1	no	—
184	C₂×Dic₁₀	C₂³×C₃	1	2	yes	—
185	C₅×SD₁₆	—	2	8	no	—
186	C₂×C₅×C₈	C₃×D₄	1	4	yes	complemented
187	C₂×C₅×C₈	C₂³×C₃	1	2	yes	—
188	#688	—	2	8	no	—
189	#687	—	2	8	no	—
190	#683	—	2	8	no	—
191	C₄×Dic₅	C₃×D₄	1	2	yes	—
192	C₄×Dic₅	C₂³×C₃	1	2	yes	—
193	C₂×#168	C₃×D₄	1	4	yes	complemented
194	C₂×#168	C₂³×C₃	1	2	yes	—
195	#677	—	2	8	no	—
196	C₂²×SD₁₆	—	5	1	no	—
197	C₂²×SD₁₆	—	5	1	no	—
198	C₂²×SD₁₆	—	5	1	no	—
199	C₂²×SD₁₆	C₃×D₅	1	1	yes	characteristic, complemented
200	C₂×C₄⋊Q₈	—	5	1	no	—
201	C₂×#127	—	5	1	no	—
202	#492	—	5	8	no	—
203	C₂×C₄×C₈	—	5	1	no	—
204	C₂²×C₃×C₅	—	4	2	no	—
205	C₂²×C₃×C₅	—	4	4	no	—
206	C₂²×C₃×C₅	—	8	4	no	—
207	C₂²×C₃×C₅	#127	1	2	yes	—
208	C₂²×C₃×C₅	C₂×SD₁₆	1	4	yes	—
209	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
210	C₂×C₃×D₅	—	4	2	no	—
211	C₂×C₃×D₅	—	4	4	no	—
212	C₂×C₃×D₅	—	8	4	no	—
213	C₃×C₄×C₅	—	4	2	no	—
214	C₃×C₄×C₅	#127	1	2	yes	—
215	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
216	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
217	C₃×Dic₅	—	4	2	no	—
218	C₃×Dic₅	C₂×SD₁₆	1	8	yes	complemented
219	C₂⁴×C₃	—	2	1	no	—
220	C₂⁴×C₃	—	10	1	no	—
221	C₂×C₃×Q₈	—	2	1	no	—
222	C₂×C₃×Q₈	—	2	2	no	—
223	C₂×C₃×Q₈	—	2	2	no	—
224	C₂×C₃×Q₈	—	5	2	no	—
225	C₂×C₃×Q₈	—	10	1	no	—
226	C₂×C₃×Q₈	—	10	2	no	—
227	C₂×C₃×Q₈	—	10	2	no	—
228	C₂×C₃×Q₈	C₂²×D₅	1	2	yes	—
229	C₂×C₃×D₄	—	2	2	no	—
230	C₂×C₃×D₄	—	2	1	no	—
231	C₂×C₃×D₄	—	2	2	no	—
232	C₂×C₃×D₄	—	5	2	no	—
233	C₂×C₃×D₄	—	10	8	no	—
234	C₂×C₃×D₄	—	10	2	no	—
235	C₂×C₃×D₄	—	10	1	no	—
236	C₂×C₃×D₄	—	10	2	no	—
237	C₂×C₃×D₄	—	20	8	no	—
238	C₂×C₃×D₄	C₂²×D₅	1	2	yes	—
239	C₂²×C₃×C₄	—	2	1	no	—
240	C₂²×C₃×C₄	—	5	2	no	—
241	C₂²×C₃×C₄	—	10	1	no	—
242	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
243	C₃×SD₁₆	—	2	8	no	—
244	C₃×SD₁₆	—	10	8	no	—
245	C₃×SD₁₆	—	10	8	no	—
246	C₃×SD₁₆	—	10	8	no	—
247	C₂×C₃×C₈	—	5	4	no	—
248	C₂×C₃×C₈	—	5	2	no	—
249	C₂×C₃×C₈	C₂²⋊D₅	1	4	yes	complemented
250	C₂×C₃×C₈	C₂²×D₅	1	2	yes	—
251	C₃×C₄⋊C₄	—	10	8	no	—
252	C₃×C₄²	—	5	2	no	—
253	C₃×C₄²	—	5	2	no	—
254	C₂³×C₅	—	2	2	no	—
255	C₂³×C₅	—	4	2	no	—
256	C₂³×C₅	—	4	4	no	—
257	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
258	C₂²×D₅	—	2	2	no	—
259	C₂²×D₅	—	4	2	no	—
260	C₂²×D₅	—	4	4	no	—
261	C₅×Q₈	—	2	2	no	—
262	C₅×Q₈	—	2	2	no	—
263	C₅×Q₈	—	4	2	no	—
264	C₅×D₄	—	2	2	no	—
265	C₅×D₄	—	2	2	no	—
266	C₅×D₄	—	4	2	no	—
267	C₂×C₄×C₅	—	2	2	no	—
268	C₂×C₄×C₅	—	4	2	no	—
269	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
270	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
271	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
272	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
273	C₂²⋊D₅	—	4	16	no	—
274	C₂×Dic₅	—	2	2	no	—
275	C₂×Dic₅	—	4	2	no	—
276	C₂×Dic₅	C₃×SD₁₆	1	8	yes	complemented
277	C₂×Dic₅	C₂×C₃×D₄	1	4	yes	—
278	D₂₀	—	2	2	no	—
279	D₂₀	—	2	2	no	—
280	D₂₀	—	4	2	no	—
281	Dic₁₀	—	2	2	no	—
282	Dic₁₀	—	2	2	no	—
283	Dic₁₀	—	4	2	no	—
284	C₅×C₈	C₂×C₃×D₄	1	4	yes	complemented
285	#168	C₂×C₃×D₄	1	4	yes	complemented
286	C₂²×Q₈	—	5	1	no	—
287	C₂²×Q₈	C₂×C₃×D₅	1	1	yes	characteristic
288	C₂²×D₄	—	5	1	no	—
289	C₂²×D₄	—	10	2	no	—
290	C₂²×D₄	C₂×C₃×D₅	1	1	yes	characteristic
291	C₂×SD₁₆	—	2	4	no	—
292	C₂×SD₁₆	—	5	4	no	—
293	C₂×SD₁₆	—	5	4	no	—
294	C₂×SD₁₆	—	5	4	no	—
295	C₂×SD₁₆	—	10	4	no	—
296	C₂×SD₁₆	—	10	4	no	—
297	C₂×SD₁₆	—	10	4	no	—
298	C₂×SD₁₆	C₂×C₃×D₅	1	4	yes	complemented
299	C₂²×C₈	—	5	1	no	—
300	C₂²×C₈	C₂×C₃×D₅	1	1	yes	characteristic
301	C₄⋊Q₈	—	5	4	no	—
302	C₄⋊Q₈	—	10	2	no	—
303	#127	—	5	4	no	—
304	#127	—	10	2	no	—
305	C₂×C₄⋊C₄	—	10	2	no	—
306	C₂×C₄²	—	5	1	no	—
307	C₄×C₈	—	5	4	no	—
308	C₂×C₃×C₅	—	8	2	no	—
309	C₂×C₃×C₅	#492	1	4	yes	complemented
310	C₂×C₃×C₅	C₂×#127	1	1	yes	characteristic
311	C₂×C₃×C₅	C₂²×SD₁₆	1	2	yes	—
312	C₃×D₅	—	8	2	no	—
313	C₂³×C₃	—	2	2	no	—
314	C₂³×C₃	—	4	4	no	—
315	C₂³×C₃	—	4	2	no	—
316	C₂³×C₃	—	10	2	no	—
317	C₂³×C₃	—	20	4	no	—
318	C₂³×C₃	—	20	2	no	—
319	C₂³×C₃	D₄×D₅	1	1	yes	characteristic
320	C₃×Q₈	—	2	2	no	—
321	C₃×Q₈	—	2	2	no	—
322	C₃×Q₈	—	4	2	no	—
323	C₃×Q₈	—	10	2	no	—
324	C₃×Q₈	—	10	2	no	—
325	C₃×Q₈	—	20	2	no	—
326	C₃×D₄	—	2	2	no	—
327	C₃×D₄	—	2	2	no	—
328	C₃×D₄	—	4	2	no	—
329	C₃×D₄	—	10	2	no	—
330	C₃×D₄	—	10	2	no	—
331	C₃×D₄	—	20	16	no	—
332	C₃×D₄	—	20	2	no	—
333	C₂×C₃×C₄	—	2	2	no	—
334	C₂×C₃×C₄	—	4	2	no	—
335	C₂×C₃×C₄	—	5	4	no	—
336	C₂×C₃×C₄	—	5	8	no	—
337	C₂×C₃×C₄	—	10	2	no	—
338	C₂×C₃×C₄	—	20	2	no	—
339	C₂×C₃×C₄	D₄×D₅	1	2	yes	—
340	C₂×C₃×C₄	D₄×D₅	1	1	yes	characteristic
341	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	2	yes	—
342	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
343	C₃×C₈	—	5	4	no	—
344	C₃×C₈	C₂×C₂²⋊D₅	1	4	yes	complemented
345	C₂²×C₅	—	4	4	no	—
346	C₂²×C₅	—	4	2	no	—
347	C₂²×C₅	—	8	4	no	—
348	C₂²×C₅	C₃×#127	1	2	yes	—
349	C₂²×C₅	C₂×C₃×SD₁₆	1	4	yes	—
350	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
351	C₂×D₅	—	4	4	no	—
352	C₂×D₅	—	4	2	no	—
353	C₂×D₅	—	8	4	no	—
354	C₄×C₅	—	4	2	no	—
355	C₄×C₅	C₃×#127	1	2	yes	—
356	C₄×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
357	C₄×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
358	Dic₅	—	4	2	no	—
359	Dic₅	C₂×C₃×SD₁₆	1	8	yes	complemented
360	C₂⁴	—	2	1	no	—
361	C₂⁴	—	10	1	no	—
362	C₂×Q₈	—	2	1	no	—
363	C₂×Q₈	—	2	2	no	—
364	C₂×Q₈	—	2	2	no	—
365	C₂×Q₈	—	5	2	no	—
366	C₂×Q₈	—	10	1	no	—
367	C₂×Q₈	—	10	2	no	—
368	C₂×Q₈	—	10	2	no	—
369	C₂×Q₈	C₂²×C₃×D₅	1	2	yes	—
370	C₂×D₄	—	2	2	no	—
371	C₂×D₄	—	2	1	no	—
372	C₂×D₄	—	2	2	no	—
373	C₂×D₄	—	5	2	no	—
374	C₂×D₄	—	10	8	no	—
375	C₂×D₄	—	10	2	no	—
376	C₂×D₄	—	10	1	no	—
377	C₂×D₄	—	10	2	no	—
378	C₂×D₄	—	20	8	no	—
379	C₂×D₄	C₂²×C₃×D₅	1	2	yes	—
380	C₂²×C₄	—	2	1	no	—
381	C₂²×C₄	—	5	2	no	—
382	C₂²×C₄	—	10	1	no	—
383	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
384	SD₁₆	—	2	8	no	—
385	SD₁₆	—	10	8	no	—
386	SD₁₆	—	10	8	no	—
387	SD₁₆	—	10	8	no	—
388	C₂×C₈	—	5	4	no	—
389	C₂×C₈	—	5	2	no	—
390	C₂×C₈	C₃×C₂²⋊D₅	1	4	yes	complemented
391	C₂×C₈	C₂²×C₃×D₅	1	2	yes	—
392	C₄⋊C₄	—	10	8	no	—
393	C₄²	—	5	2	no	—
394	C₄²	—	5	2	no	—
395	C₃×C₅	C₂×#492	1	1	yes	characteristic, complemented, Hall
396	C₂²×C₃	—	4	4	no	—
397	C₂²×C₃	—	4	2	no	—
398	C₂²×C₃	—	8	4	no	—
399	C₂²×C₃	—	20	4	no	—
400	C₂²×C₃	—	20	2	no	—
401	C₂²×C₃	—	40	4	no	—
402	C₂²×C₃	D₅×SD₁₆	1	4	yes	—
403	C₂²×C₃	#4086	1	2	yes	—
404	C₂²×C₃	C₂×D₄×D₅	1	1	yes	characteristic
405	C₃×C₄	—	4	2	no	—
406	C₃×C₄	—	5	8	no	—
407	C₃×C₄	—	20	2	no	—
408	C₃×C₄	#4086	1	2	yes	—
409	C₃×C₄	C₂×D₄×D₅	1	1	yes	characteristic
410	C₃×C₄	C₂²×C₂²⋊D₅	1	1	yes	characteristic
411	C₂×C₅	—	8	2	no	—
412	C₂×C₅	C₃×#492	1	4	yes	complemented
413	C₂×C₅	C₂×C₃×#127	1	1	yes	characteristic
414	C₂×C₅	C₂²×C₃×SD₁₆	1	2	yes	—
415	D₅	—	8	2	no	—
416	C₂³	—	2	2	no	—
417	C₂³	—	4	2	no	—
418	C₂³	—	4	4	no	—
419	C₂³	—	10	2	no	—
420	C₂³	—	20	2	no	—
421	C₂³	—	20	4	no	—
422	C₂³	C₃×D₄×D₅	1	1	yes	characteristic
423	Q₈	—	2	2	no	—
424	Q₈	—	2	2	no	—
425	Q₈	—	4	2	no	—
426	Q₈	—	10	2	no	—
427	Q₈	—	10	2	no	—
428	Q₈	—	20	2	no	—
429	D₄	—	2	2	no	—
430	D₄	—	2	2	no	—
431	D₄	—	4	2	no	—
432	D₄	—	10	2	no	—
433	D₄	—	10	2	no	—
434	D₄	—	20	16	no	—
435	D₄	—	20	2	no	—
436	C₂×C₄	—	2	2	no	—
437	C₂×C₄	—	4	2	no	—
438	C₂×C₄	—	5	4	no	—
439	C₂×C₄	—	5	8	no	—
440	C₂×C₄	—	10	2	no	—
441	C₂×C₄	—	20	2	no	—
442	C₂×C₄	C₃×D₄×D₅	1	1	yes	characteristic
443	C₂×C₄	C₃×D₄×D₅	1	2	yes	—
444	C₂×C₄	C₂×C₃×C₂²⋊D₅	1	2	yes	—
445	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
446	C₈	—	5	4	no	—
447	C₈	C₂×C₃×C₂²⋊D₅	1	4	yes	complemented
448	C₂×C₃	—	8	2	no	—
449	C₂×C₃	—	40	2	no	—
450	C₂×C₃	#65464	1	4	yes	direct product factor
451	C₂×C₃	C₂×D₅×SD₁₆	1	2	yes	—
452	C₂×C₃	C₂×#4086	1	1	yes	characteristic
453	C₅	C₂×C₃×#492	1	1	yes	characteristic, complemented, Sylow
454	C₂²	—	4	2	no	—
455	C₂²	—	4	4	no	—
456	C₂²	—	8	4	no	—
457	C₂²	—	20	2	no	—
458	C₂²	—	20	4	no	—
459	C₂²	—	40	4	no	—
460	C₂²	C₃×D₅×SD₁₆	1	4	yes	—
461	C₂²	C₃×#4086	1	2	yes	—
462	C₂²	C₂×C₃×D₄×D₅	1	1	yes	characteristic
463	C₄	—	4	2	no	—
464	C₄	—	5	8	no	—
465	C₄	—	20	2	no	—
466	C₄	C₃×#4086	1	2	yes	—
467	C₄	C₂×C₃×D₄×D₅	1	1	yes	characteristic
468	C₄	C₂²×C₃×C₂²⋊D₅	1	1	yes	characteristic
469	C₃	C₂×#65464	1	1	yes	characteristic, direct product factor, Sylow
470	C₂	—	8	2	no	—
471	C₂	—	40	2	no	—
472	C₂	C₃×#65464	1	4	yes	direct product factor
473	C₂	C₂×C₃×D₅×SD₁₆	1	2	yes	—
474	C₂	C₂×C₃×#4086	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₃	D₄×D₅
commutator, cosocle	C₂×C₄×C₅	C₂⁴×C₃
Frattini	C₂×C₄	C₂³×C₃×D₅
Fitting	C₂²×C₃×C₅×SD₁₆	C₂
socle	C₂³×C₃×C₅	C₂×D₄
prime radical	C₂×C₃×#4086	C₂
hypercenter	C₂²×C₃×SD₁₆	D₅
hypocenter	C₅	C₂×C₃×#492
LCS	G ▷ C₂×C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂³×C₃ ◁ C₂²×C₃×C₄ ◁ C₂²×C₃×SD₁₆

Complements

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

N	H ≅ G/N	type
1. C₂²×C₃×C₅×SD₁₆	C₂	semidirect
2. C₂×C₃×#4090	C₂	semidirect
3. C₂²×C₃×#688	C₂	semidirect
5. C₂²×C₃×#687	C₂	semidirect
6. C₂²×C₃×#677	C₂	semidirect
7. C₃×#65464	C₂	direct (N × H)
8. C₂×C₃×C₈×Dic₅	C₂	semidirect
9. C₂×#65464	C₃	direct (N × H)
16. C₂×C₃×C₅×SD₁₆	C₂²	semidirect
19. C₃×#4090	C₂²	semidirect
21. C₂×C₃×#688	C₂²	semidirect
25. C₂×C₃×#687	C₂²	semidirect
30. C₂×C₃×#677	C₂²	semidirect
31. C₃×C₈×Dic₅	C₂²	semidirect
33. C₂²×C₅×SD₁₆	C₂×C₃	semidirect
34. C₂×#4090	C₂×C₃	semidirect
35. C₂²×#688	C₂×C₃	semidirect
37. C₂²×#687	C₂×C₃	semidirect
38. C₂²×#677	C₂×C₃	semidirect
39. #65464	C₂×C₃	direct (N × H)
40. C₂×C₈×Dic₅	C₂×C₃	semidirect
66. C₂×C₃×C₅×C₈	D₄	semidirect
73. C₂×C₃×#168	D₄	semidirect
79. C₂²×C₃×SD₁₆	D₅	semidirect
90. C₂×C₅×SD₁₆	C₂²×C₃	semidirect
93. #4090	C₂²×C₃	semidirect
95. C₂×#688	C₂²×C₃	semidirect
99. C₂×#687	C₂²×C₃	semidirect
104. C₂×#677	C₂²×C₃	semidirect
105. C₈×Dic₅	C₂²×C₃	semidirect
129. C₂×C₃×Dic₅	SD₁₆	semidirect
137. C₃×C₅×C₈	C₂×D₄	semidirect
138. C₃×#168	C₂×D₄	semidirect
151. C₂×C₃×SD₁₆	C₂×D₅	semidirect
186. C₂×C₅×C₈	C₃×D₄	semidirect
193. C₂×#168	C₃×D₄	semidirect
199. C₂²×SD₁₆	C₃×D₅	semidirect
218. C₃×Dic₅	C₂×SD₁₆	semidirect
249. C₂×C₃×C₈	C₂²⋊D₅	semidirect
276. C₂×Dic₅	C₃×SD₁₆	semidirect
284. C₅×C₈	C₂×C₃×D₄	semidirect
285. #168	C₂×C₃×D₄	semidirect
298. C₂×SD₁₆	C₂×C₃×D₅	semidirect
309. C₂×C₃×C₅	#492	semidirect
344. C₃×C₈	C₂×C₂²⋊D₅	semidirect
359. Dic₅	C₂×C₃×SD₁₆	semidirect
390. C₂×C₈	C₃×C₂²⋊D₅	semidirect
395. C₃×C₅	C₂×#492	semidirect
412. C₂×C₅	C₃×#492	semidirect
447. C₈	C₂×C₃×C₂²⋊D₅	semidirect
450. C₂×C₃	#65464	direct (N × H)
453. C₅	C₂×C₃×#492	semidirect
469. C₃	C₂×#65464	direct (N × H)
472. C₂	C₃×#65464	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×SD₁₆	2
C₂×C₃×#4090	2
C₂²×C₃×#688	2
C₂×C₃×#4086	2
C₂²×C₃×#687	2
C₂²×C₃×#677	2
C₃×#65464	2
C₂×C₃×C₈×Dic₅	2
C₂×#65464	3
C₂×C₃×#492	5

Subgroups — C2×C3×#65464 #14438725

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#65464 #14438725