Subgroups — C₂×C₃×#65457 #14438827

Order 1920.

1184 conjugacy classes of subgroups.

The subgroup lattice has 468 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×#4093	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₃×#689	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₃×#4082	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂²×C₃×#686	C₂	1	1	yes	maximal, characteristic
6	C₂²×C₃×#677	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#65457	C₂	1	8	yes	maximal, direct product factor
8	C₂×C₃×C₈×Dic₅	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#65457	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×D₂₀	C₂²	1	1	yes	characteristic
13	C₂²×C₃×Dic₁₀	C₂²	1	1	yes	characteristic
14	C₂×C₃×C₅×SD₁₆	—	2	4	no	—
15	C₂×C₃×C₅×SD₁₆	C₂²	1	4	yes	complemented
16	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
17	C₂×C₃×C₂²⋊Dic₅	—	2	2	no	—
18	C₃×#4093	—	2	2	no	—
19	C₃×#4093	C₂²	1	4	yes	complemented
20	C₂×C₃×#689	—	2	4	no	—
21	C₂×C₃×#689	C₂²	1	4	yes	complemented
22	C₃×#4082	—	2	2	no	—
23	C₃×#4082	C₂²	1	4	yes	complemented
24	C₂×C₃×#686	—	2	4	no	—
25	C₂×C₃×#686	C₂²	1	4	yes	—
26	C₂×C₃×#685	—	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×#495	—	5	1	no	maximal, Hall
33	C₂²×C₅×SD₁₆	C₂×C₃	1	1	yes	characteristic, complemented
34	C₂×#4093	C₂×C₃	1	1	yes	characteristic, complemented
35	C₂²×#689	C₂×C₃	1	1	yes	characteristic, complemented
36	C₂×#4082	C₂×C₃	1	1	yes	characteristic, complemented
37	C₂²×#686	C₂×C₃	1	1	yes	characteristic
38	C₂²×#677	C₂×C₃	1	1	yes	characteristic, complemented
39	#65457	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	C₂²×C₃×Dic₅	—	2	1	no	—
54	C₂²×C₃×Dic₅	D₄	1	2	yes	—
55	C₂×C₃×D₂₀	—	2	2	no	—
56	C₂×C₃×D₂₀	—	2	2	no	—
57	C₂×C₃×D₂₀	—	2	1	no	—
58	C₂×C₃×D₂₀	C₂³	1	2	yes	—
59	C₂×C₃×Dic₁₀	—	2	2	no	—
60	C₂×C₃×Dic₁₀	—	2	2	no	—
61	C₂×C₃×Dic₁₀	—	2	1	no	—
62	C₂×C₃×Dic₁₀	C₂³	1	2	yes	—
63	C₃×C₅×SD₁₆	—	2	8	no	—
64	C₂×C₃×C₅×C₈	D₄	1	4	yes	—
65	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
66	C₃×C₂²⋊Dic₅	—	2	8	no	—
67	C₃×#689	—	2	8	no	—
68	C₃×#686	—	2	8	no	—
69	C₃×#685	—	2	8	no	—
70	C₃×C₄×Dic₅	D₄	1	2	yes	—
71	C₃×C₄×Dic₅	C₂³	1	2	yes	—
72	C₂×C₃×#168	D₄	1	4	yes	—
73	C₂×C₃×#168	C₂³	1	2	yes	—
74	C₃×#677	—	2	8	no	—
75	C₂²×C₃×Q₁₆	—	5	1	no	—
76	C₂²×C₃×SD₁₆	—	5	1	no	—
77	C₂²×C₃×SD₁₆	D₅	1	1	yes	characteristic, complemented
78	C₂²×C₃×D₈	—	5	1	no	—
79	C₂×C₃×#124	—	5	1	no	—
80	C₂×C₃×#124	—	5	1	no	—
81	C₃×#495	—	5	8	no	—
82	C₂×C₃×C₄×C₈	—	5	1	no	—
83	C₂²×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic
84	C₂²×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
85	C₂²×D₂₀	C₂²×C₃	1	1	yes	characteristic
86	C₂²×Dic₁₀	C₂²×C₃	1	1	yes	characteristic
87	C₂×C₅×SD₁₆	—	2	4	no	—
88	C₂×C₅×SD₁₆	C₂²×C₃	1	4	yes	complemented
89	C₂²×C₅×C₈	C₂²×C₃	1	1	yes	characteristic
90	C₂×C₂²⋊Dic₅	—	2	2	no	—
91	#4093	—	2	2	no	—
92	#4093	C₂²×C₃	1	4	yes	complemented
93	C₂×#689	—	2	4	no	—
94	C₂×#689	C₂²×C₃	1	4	yes	complemented
95	#4082	—	2	2	no	—
96	#4082	C₂²×C₃	1	4	yes	complemented
97	C₂×#686	—	2	4	no	—
98	C₂×#686	C₂²×C₃	1	4	yes	—
99	C₂×#685	—	2	2	no	—
100	C₂×C₄×Dic₅	C₂²×C₃	1	1	yes	characteristic
101	C₂²×#168	C₂²×C₃	1	1	yes	characteristic
102	C₂×#677	—	2	4	no	—
103	C₂×#677	C₂²×C₃	1	4	yes	complemented
104	C₈×Dic₅	C₂²×C₃	1	4	yes	complemented
105	C₂×#495	—	5	1	no	Sylow
106	C₂³×C₃×C₅	—	2	2	no	—
107	C₂³×C₃×C₅	—	4	2	no	—
108	C₂³×C₃×C₅	—	4	4	no	—
109	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
110	C₂²×C₃×D₅	—	2	2	no	—
111	C₂²×C₃×D₅	—	4	2	no	—
112	C₂²×C₃×D₅	—	4	4	no	—
113	C₃×C₅×Q₈	—	2	2	no	—
114	C₃×C₅×Q₈	—	2	2	no	—
115	C₃×C₅×Q₈	—	4	2	no	—
116	C₃×C₅×D₄	—	2	2	no	—
117	C₃×C₅×D₄	—	2	2	no	—
118	C₃×C₅×D₄	—	4	2	no	—
119	C₂×C₃×C₄×C₅	—	2	2	no	—
120	C₂×C₃×C₄×C₅	—	4	2	no	—
121	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
122	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
123	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
124	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
125	C₂×C₃×Dic₅	—	2	4	no	—
126	C₂×C₃×Dic₅	—	2	2	no	—
127	C₂×C₃×Dic₅	—	4	2	no	—
128	C₂×C₃×Dic₅	C₂×D₄	1	4	yes	—
129	C₃×D₂₀	—	2	2	no	—
130	C₃×D₂₀	—	2	2	no	—
131	C₃×D₂₀	—	4	2	no	—
132	C₃×Dic₁₀	—	2	2	no	—
133	C₃×Dic₁₀	—	2	2	no	—
134	C₃×Dic₁₀	—	4	2	no	—
135	C₃×C₅×C₈	C₂×D₄	1	4	yes	—
136	C₃×#168	C₂×D₄	1	4	yes	—
137	C₂²×C₃×Q₈	—	5	1	no	—
138	C₂²×C₃×Q₈	C₂×D₅	1	1	yes	characteristic
139	C₂²×C₃×D₄	—	5	1	no	—
140	C₂²×C₃×D₄	C₂×D₅	1	1	yes	characteristic
141	C₂×C₃×Q₁₆	—	5	4	no	—
142	C₂×C₃×Q₁₆	—	10	4	no	—
143	C₂×C₃×SD₁₆	—	2	4	no	—
144	C₂×C₃×SD₁₆	—	5	4	no	—
145	C₂×C₃×SD₁₆	—	10	4	no	—
146	C₂×C₃×SD₁₆	C₂×D₅	1	4	yes	complemented
147	C₂×C₃×D₈	—	5	4	no	—
148	C₂×C₃×D₈	—	10	4	no	—
149	C₂²×C₃×C₈	—	5	1	no	—
150	C₂²×C₃×C₈	C₂×D₅	1	1	yes	characteristic
151	C₃×#124	—	5	4	no	—
152	C₃×#124	—	5	4	no	—
153	C₃×#124	—	10	2	no	—
154	C₃×#124	—	10	2	no	—
155	C₂×C₃×C₂²⋊C₄	—	10	2	no	—
156	C₂×C₃×C₂²⋊C₄	—	10	2	no	—
157	C₂×C₃×C₄²	—	5	1	no	—
158	C₃×C₄×C₈	—	5	4	no	—
159	C₂⁴×C₅	—	2	1	no	—
160	C₂³×D₅	—	2	1	no	—
161	C₂×C₅×Q₈	—	2	1	no	—
162	C₂×C₅×Q₈	—	2	2	no	—
163	C₂×C₅×Q₈	—	2	2	no	—
164	C₂×C₅×Q₈	C₂³×C₃	1	2	yes	—
165	C₂×C₅×D₄	—	2	2	no	—
166	C₂×C₅×D₄	—	2	2	no	—
167	C₂×C₅×D₄	—	2	1	no	—
168	C₂×C₅×D₄	C₂³×C₃	1	2	yes	—
169	C₂²×C₄×C₅	—	2	1	no	—
170	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
171	C₂²×Dic₅	—	2	1	no	—
172	C₂²×Dic₅	C₃×D₄	1	2	yes	—
173	C₂×D₂₀	—	2	2	no	—
174	C₂×D₂₀	—	2	2	no	—
175	C₂×D₂₀	—	2	1	no	—
176	C₂×D₂₀	C₂³×C₃	1	2	yes	—
177	C₂×Dic₁₀	—	2	2	no	—
178	C₂×Dic₁₀	—	2	2	no	—
179	C₂×Dic₁₀	—	2	1	no	—
180	C₂×Dic₁₀	C₂³×C₃	1	2	yes	—
181	C₅×SD₁₆	—	2	8	no	—
182	C₂×C₅×C₈	C₃×D₄	1	4	yes	—
183	C₂×C₅×C₈	C₂³×C₃	1	2	yes	—
184	C₂²⋊Dic₅	—	2	8	no	—
185	#689	—	2	8	no	—
186	#686	—	2	8	no	—
187	#685	—	2	8	no	—
188	C₄×Dic₅	C₃×D₄	1	2	yes	—
189	C₄×Dic₅	C₂³×C₃	1	2	yes	—
190	C₂×#168	C₃×D₄	1	4	yes	—
191	C₂×#168	C₂³×C₃	1	2	yes	—
192	#677	—	2	8	no	—
193	C₂²×Q₁₆	—	5	1	no	—
194	C₂²×SD₁₆	—	5	1	no	—
195	C₂²×SD₁₆	C₃×D₅	1	1	yes	characteristic, complemented
196	C₂²×D₈	—	5	1	no	—
197	C₂×#124	—	5	1	no	—
198	C₂×#124	—	5	1	no	—
199	#495	—	5	8	no	—
200	C₂×C₄×C₈	—	5	1	no	—
201	C₂²×C₃×C₅	—	4	2	no	—
202	C₂²×C₃×C₅	—	4	4	no	—
203	C₂²×C₃×C₅	—	8	4	no	—
204	C₂²×C₃×C₅	#127	1	2	yes	—
205	C₂²×C₃×C₅	#135	1	4	yes	—
206	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
207	C₂×C₃×D₅	—	4	2	no	—
208	C₂×C₃×D₅	—	4	4	no	—
209	C₂×C₃×D₅	—	8	4	no	—
210	C₃×C₄×C₅	—	4	2	no	—
211	C₃×C₄×C₅	#127	1	2	yes	—
212	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
213	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
214	C₃×Dic₅	—	2	4	no	—
215	C₃×Dic₅	—	4	2	no	—
216	C₂⁴×C₃	—	2	1	no	—
217	C₂⁴×C₃	—	10	1	no	—
218	C₂×C₃×Q₈	—	2	1	no	—
219	C₂×C₃×Q₈	—	2	2	no	—
220	C₂×C₃×Q₈	—	2	2	no	—
221	C₂×C₃×Q₈	—	5	2	no	—
222	C₂×C₃×Q₈	—	10	1	no	—
223	C₂×C₃×Q₈	—	10	2	no	—
224	C₂×C₃×Q₈	—	10	2	no	—
225	C₂×C₃×Q₈	C₂²×D₅	1	2	yes	—
226	C₂×C₃×D₄	—	2	2	no	—
227	C₂×C₃×D₄	—	2	1	no	—
228	C₂×C₃×D₄	—	2	2	no	—
229	C₂×C₃×D₄	—	5	2	no	—
230	C₂×C₃×D₄	—	10	2	no	—
231	C₂×C₃×D₄	—	10	1	no	—
232	C₂×C₃×D₄	—	10	2	no	—
233	C₂×C₃×D₄	C₂²×D₅	1	2	yes	—
234	C₂²×C₃×C₄	—	2	1	no	—
235	C₂²×C₃×C₄	—	5	2	no	—
236	C₂²×C₃×C₄	—	10	1	no	—
237	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
238	C₃×Q₁₆	—	10	8	no	—
239	C₃×SD₁₆	—	2	8	no	—
240	C₃×SD₁₆	—	10	8	no	—
241	C₃×D₈	—	10	8	no	—
242	C₂×C₃×C₈	—	5	4	no	—
243	C₂×C₃×C₈	—	5	2	no	—
244	C₂×C₃×C₈	C₂²⋊D₅	1	4	yes	—
245	C₂×C₃×C₈	C₂²×D₅	1	2	yes	—
246	C₃×C₂²⋊C₄	—	10	8	no	—
247	C₃×C₂²⋊C₄	—	10	8	no	—
248	C₃×C₄²	—	5	2	no	—
249	C₃×C₄²	—	5	2	no	—
250	C₂³×C₅	—	2	2	no	—
251	C₂³×C₅	—	4	2	no	—
252	C₂³×C₅	—	4	4	no	—
253	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
254	C₂²×D₅	—	2	2	no	—
255	C₂²×D₅	—	4	2	no	—
256	C₂²×D₅	—	4	4	no	—
257	C₅×Q₈	—	2	2	no	—
258	C₅×Q₈	—	2	2	no	—
259	C₅×Q₈	—	4	2	no	—
260	C₅×D₄	—	2	2	no	—
261	C₅×D₄	—	2	2	no	—
262	C₅×D₄	—	4	2	no	—
263	C₂×C₄×C₅	—	2	2	no	—
264	C₂×C₄×C₅	—	4	2	no	—
265	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
266	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
267	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
268	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
269	C₂×Dic₅	—	2	4	no	—
270	C₂×Dic₅	—	2	2	no	—
271	C₂×Dic₅	—	4	2	no	—
272	C₂×Dic₅	C₂×C₃×D₄	1	4	yes	—
273	D₂₀	—	2	2	no	—
274	D₂₀	—	2	2	no	—
275	D₂₀	—	4	2	no	—
276	Dic₁₀	—	2	2	no	—
277	Dic₁₀	—	2	2	no	—
278	Dic₁₀	—	4	2	no	—
279	C₅×C₈	C₂×C₃×D₄	1	4	yes	—
280	#168	C₂×C₃×D₄	1	4	yes	—
281	C₂²×Q₈	—	5	1	no	—
282	C₂²×Q₈	C₂×C₃×D₅	1	1	yes	characteristic
283	C₂²×D₄	—	5	1	no	—
284	C₂²×D₄	C₂×C₃×D₅	1	1	yes	characteristic
285	C₂×Q₁₆	—	5	4	no	—
286	C₂×Q₁₆	—	10	4	no	—
287	C₂×SD₁₆	—	2	4	no	—
288	C₂×SD₁₆	—	5	4	no	—
289	C₂×SD₁₆	—	10	4	no	—
290	C₂×SD₁₆	C₂×C₃×D₅	1	4	yes	complemented
291	C₂×D₈	—	5	4	no	—
292	C₂×D₈	—	10	4	no	—
293	C₂²×C₈	—	5	1	no	—
294	C₂²×C₈	C₂×C₃×D₅	1	1	yes	characteristic
295	#124	—	5	4	no	—
296	#124	—	5	4	no	—
297	#124	—	10	2	no	—
298	#124	—	10	2	no	—
299	C₂×C₂²⋊C₄	—	10	2	no	—
300	C₂×C₂²⋊C₄	—	10	2	no	—
301	C₂×C₄²	—	5	1	no	—
302	C₄×C₈	—	5	4	no	—
303	C₂×C₃×C₅	—	8	2	no	—
304	C₂×C₃×C₅	#495	1	4	yes	complemented
305	C₂×C₃×C₅	C₂×#127	1	1	yes	characteristic
306	C₂×C₃×C₅	C₂×#135	1	2	yes	—
307	C₃×D₅	—	8	2	no	—
308	C₂³×C₃	—	2	2	no	—
309	C₂³×C₃	—	4	4	no	—
310	C₂³×C₃	—	4	2	no	—
311	C₂³×C₃	—	10	2	no	—
312	C₂³×C₃	—	20	4	no	—
313	C₂³×C₃	—	20	2	no	—
314	C₂³×C₃	D₄×D₅	1	1	yes	characteristic
315	C₃×Q₈	—	2	2	no	—
316	C₃×Q₈	—	2	2	no	—
317	C₃×Q₈	—	4	2	no	—
318	C₃×Q₈	—	10	2	no	—
319	C₃×Q₈	—	10	2	no	—
320	C₃×Q₈	—	20	2	no	—
321	C₃×D₄	—	2	2	no	—
322	C₃×D₄	—	2	2	no	—
323	C₃×D₄	—	4	2	no	—
324	C₃×D₄	—	10	2	no	—
325	C₃×D₄	—	10	2	no	—
326	C₃×D₄	—	20	2	no	—
327	C₂×C₃×C₄	—	2	2	no	—
328	C₂×C₃×C₄	—	4	2	no	—
329	C₂×C₃×C₄	—	5	4	no	—
330	C₂×C₃×C₄	—	10	4	no	—
331	C₂×C₃×C₄	—	10	2	no	—
332	C₂×C₃×C₄	—	20	2	no	—
333	C₂×C₃×C₄	D₄×D₅	1	2	yes	—
334	C₂×C₃×C₄	D₄×D₅	1	1	yes	characteristic
335	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	2	yes	—
336	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
337	C₃×C₈	—	5	4	no	—
338	C₃×C₈	C₂×C₂²⋊D₅	1	4	yes	—
339	C₂²×C₅	—	4	4	no	—
340	C₂²×C₅	—	4	2	no	—
341	C₂²×C₅	—	8	4	no	—
342	C₂²×C₅	C₃×#127	1	2	yes	—
343	C₂²×C₅	C₃×#135	1	4	yes	—
344	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
345	C₂×D₅	—	4	4	no	—
346	C₂×D₅	—	4	2	no	—
347	C₂×D₅	—	8	4	no	—
348	C₄×C₅	—	4	2	no	—
349	C₄×C₅	C₃×#127	1	2	yes	—
350	C₄×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
351	C₄×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
352	Dic₅	—	2	4	no	—
353	Dic₅	—	4	2	no	—
354	C₂⁴	—	2	1	no	—
355	C₂⁴	—	10	1	no	—
356	C₂×Q₈	—	2	1	no	—
357	C₂×Q₈	—	2	2	no	—
358	C₂×Q₈	—	2	2	no	—
359	C₂×Q₈	—	5	2	no	—
360	C₂×Q₈	—	10	1	no	—
361	C₂×Q₈	—	10	2	no	—
362	C₂×Q₈	—	10	2	no	—
363	C₂×Q₈	C₂²×C₃×D₅	1	2	yes	—
364	C₂×D₄	—	2	2	no	—
365	C₂×D₄	—	2	1	no	—
366	C₂×D₄	—	2	2	no	—
367	C₂×D₄	—	5	2	no	—
368	C₂×D₄	—	10	2	no	—
369	C₂×D₄	—	10	1	no	—
370	C₂×D₄	—	10	2	no	—
371	C₂×D₄	C₂²×C₃×D₅	1	2	yes	—
372	C₂²×C₄	—	2	1	no	—
373	C₂²×C₄	—	5	2	no	—
374	C₂²×C₄	—	10	1	no	—
375	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
376	Q₁₆	—	10	8	no	—
377	SD₁₆	—	2	8	no	—
378	SD₁₆	—	10	8	no	—
379	D₈	—	10	8	no	—
380	C₂×C₈	—	5	4	no	—
381	C₂×C₈	—	5	2	no	—
382	C₂×C₈	C₃×C₂²⋊D₅	1	4	yes	—
383	C₂×C₈	C₂²×C₃×D₅	1	2	yes	—
384	C₂²⋊C₄	—	10	8	no	—
385	C₂²⋊C₄	—	10	8	no	—
386	C₄²	—	5	2	no	—
387	C₄²	—	5	2	no	—
388	C₃×C₅	C₂×#495	1	1	yes	characteristic, complemented, Hall
389	C₂²×C₃	—	4	4	no	—
390	C₂²×C₃	—	4	2	no	—
391	C₂²×C₃	—	8	4	no	—
392	C₂²×C₃	—	20	4	no	—
393	C₂²×C₃	—	20	2	no	—
394	C₂²×C₃	—	40	4	no	—
395	C₂²×C₃	#4062	1	4	yes	—
396	C₂²×C₃	#4086	1	2	yes	—
397	C₂²×C₃	C₂×D₄×D₅	1	1	yes	characteristic
398	C₃×C₄	—	4	2	no	—
399	C₃×C₄	—	10	4	no	—
400	C₃×C₄	—	20	2	no	—
401	C₃×C₄	#4086	1	2	yes	—
402	C₃×C₄	C₂×D₄×D₅	1	1	yes	characteristic
403	C₃×C₄	C₂²×C₂²⋊D₅	1	1	yes	characteristic
404	C₂×C₅	—	8	2	no	—
405	C₂×C₅	C₃×#495	1	4	yes	complemented
406	C₂×C₅	C₂×C₃×#127	1	1	yes	characteristic
407	C₂×C₅	C₂×C₃×#135	1	2	yes	—
408	D₅	—	8	2	no	—
409	C₂³	—	2	2	no	—
410	C₂³	—	4	2	no	—
411	C₂³	—	4	4	no	—
412	C₂³	—	10	2	no	—
413	C₂³	—	20	2	no	—
414	C₂³	—	20	4	no	—
415	C₂³	C₃×D₄×D₅	1	1	yes	characteristic
416	Q₈	—	2	2	no	—
417	Q₈	—	2	2	no	—
418	Q₈	—	4	2	no	—
419	Q₈	—	10	2	no	—
420	Q₈	—	10	2	no	—
421	Q₈	—	20	2	no	—
422	D₄	—	2	2	no	—
423	D₄	—	2	2	no	—
424	D₄	—	4	2	no	—
425	D₄	—	10	2	no	—
426	D₄	—	10	2	no	—
427	D₄	—	20	2	no	—
428	C₂×C₄	—	2	2	no	—
429	C₂×C₄	—	4	2	no	—
430	C₂×C₄	—	5	4	no	—
431	C₂×C₄	—	10	4	no	—
432	C₂×C₄	—	10	2	no	—
433	C₂×C₄	—	20	2	no	—
434	C₂×C₄	C₃×D₄×D₅	1	1	yes	characteristic
435	C₂×C₄	C₃×D₄×D₅	1	2	yes	—
436	C₂×C₄	C₂×C₃×C₂²⋊D₅	1	2	yes	—
437	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
438	C₈	—	5	4	no	—
439	C₈	C₂×C₃×C₂²⋊D₅	1	4	yes	—
440	C₂×C₃	—	8	2	no	—
441	C₂×C₃	—	40	2	no	—
442	C₂×C₃	#65457	1	4	yes	direct product factor
443	C₂×C₃	C₂×#4062	1	2	yes	—
444	C₂×C₃	C₂×#4086	1	1	yes	characteristic
445	C₅	C₂×C₃×#495	1	1	yes	characteristic, complemented, Sylow
446	C₂²	—	4	2	no	—
447	C₂²	—	4	4	no	—
448	C₂²	—	8	4	no	—
449	C₂²	—	20	2	no	—
450	C₂²	—	20	4	no	—
451	C₂²	—	40	4	no	—
452	C₂²	C₃×#4062	1	4	yes	—
453	C₂²	C₃×#4086	1	2	yes	—
454	C₂²	C₂×C₃×D₄×D₅	1	1	yes	characteristic
455	C₄	—	4	2	no	—
456	C₄	—	10	4	no	—
457	C₄	—	20	2	no	—
458	C₄	C₃×#4086	1	2	yes	—
459	C₄	C₂×C₃×D₄×D₅	1	1	yes	characteristic
460	C₄	C₂²×C₃×C₂²⋊D₅	1	1	yes	characteristic
461	C₃	C₂×#65457	1	1	yes	characteristic, direct product factor, Sylow
462	C₂	—	8	2	no	—
463	C₂	—	40	2	no	—
464	C₂	C₃×#65457	1	4	yes	direct product factor
465	C₂	C₂×C₃×#4062	1	2	yes	—
466	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	C₂²×C₃×#686	C₂
hypercenter	C₂²×C₃×SD₁₆	D₅
hypocenter	C₅	C₂×C₃×#495
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×#4093	C₂	semidirect
3. C₂²×C₃×#689	C₂	semidirect
4. C₂×C₃×#4082	C₂	semidirect
6. C₂²×C₃×#677	C₂	semidirect
7. C₃×#65457	C₂	direct (N × H)
8. C₂×C₃×C₈×Dic₅	C₂	semidirect
9. C₂×#65457	C₃	direct (N × H)
15. C₂×C₃×C₅×SD₁₆	C₂²	semidirect
19. C₃×#4093	C₂²	semidirect
21. C₂×C₃×#689	C₂²	semidirect
23. C₃×#4082	C₂²	semidirect
30. C₂×C₃×#677	C₂²	semidirect
31. C₃×C₈×Dic₅	C₂²	semidirect
33. C₂²×C₅×SD₁₆	C₂×C₃	semidirect
34. C₂×#4093	C₂×C₃	semidirect
35. C₂²×#689	C₂×C₃	semidirect
36. C₂×#4082	C₂×C₃	semidirect
38. C₂²×#677	C₂×C₃	semidirect
39. #65457	C₂×C₃	direct (N × H)
40. C₂×C₈×Dic₅	C₂×C₃	semidirect
77. C₂²×C₃×SD₁₆	D₅	semidirect
88. C₂×C₅×SD₁₆	C₂²×C₃	semidirect
92. #4093	C₂²×C₃	semidirect
94. C₂×#689	C₂²×C₃	semidirect
96. #4082	C₂²×C₃	semidirect
103. C₂×#677	C₂²×C₃	semidirect
104. C₈×Dic₅	C₂²×C₃	semidirect
146. C₂×C₃×SD₁₆	C₂×D₅	semidirect
195. C₂²×SD₁₆	C₃×D₅	semidirect
290. C₂×SD₁₆	C₂×C₃×D₅	semidirect
304. C₂×C₃×C₅	#495	semidirect
388. C₃×C₅	C₂×#495	semidirect
405. C₂×C₅	C₃×#495	semidirect
442. C₂×C₃	#65457	direct (N × H)
445. C₅	C₂×C₃×#495	semidirect
461. C₃	C₂×#65457	direct (N × H)
464. C₂	C₃×#65457	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×#4093	2
C₂²×C₃×#689	2
C₂×C₃×#4082	2
C₂²×C₃×#686	2
C₂²×C₃×#677	2
C₃×#65457	2
C₂×C₃×C₈×Dic₅	2
C₂×#65457	3
C₂×C₃×#495	5

Subgroups — C2×C3×#65457 #14438827

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#65457 #14438827