Subgroups — C₂×C₃×#65506 #14423182

Order 1920.

2096 conjugacy classes of subgroups.

The subgroup lattice has 480 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₃×C₅×D₄	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₃×#686	C₂	1	2	yes	maximal, complemented
3	C₂×C₃×#4076	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#65506	C₂	1	8	yes	maximal, direct product factor
5	C₂×C₃×#3964	C₂	1	2	yes	maximal, complemented
6	C₂×C₃×C₂²⋊#168	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#65506	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₂⁵×C₃×C₅	—	2	1	no	—
9	C₂²×C₃×C₅×D₄	—	2	8	no	—
10	C₂²×C₃×C₅×D₄	—	2	1	no	—
11	C₂²×C₃×C₅×D₄	—	2	2	no	—
12	C₂²×C₃×C₅×D₄	C₂²	1	2	yes	—
13	C₂²×C₃×C₅×D₄	C₂²	1	4	yes	complemented
14	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
15	C₂²×C₃×C₂²⋊D₅	—	2	1	no	—
16	C₂²×C₃×D₂₀	C₂²	1	1	yes	characteristic, complemented
17	C₂×C₃×#686	—	2	8	no	—
18	C₂×C₃×#686	C₂²	1	8	yes	complemented
19	C₃×#4076	—	2	2	no	—
20	C₃×#4076	C₂²	1	4	yes	complemented
21	C₂×C₃×#685	—	2	1	no	—
22	C₂×C₃×C₄⋊Dic₅	C₂²	1	1	yes	characteristic, complemented
23	C₂²×C₃×#168	C₂²	1	2	yes	complemented
24	C₃×#3964	C₂²	1	8	yes	complemented
25	C₃×C₂²⋊#168	C₂²	1	4	yes	complemented
26	C₂×C₃×#447	—	5	1	no	maximal, Hall
27	C₂³×C₅×D₄	C₂×C₃	1	1	yes	characteristic, complemented
28	C₂²×#686	C₂×C₃	1	2	yes	complemented
29	C₂×#4076	C₂×C₃	1	1	yes	characteristic, complemented
30	#65506	C₂×C₃	1	8	yes	direct product factor
31	C₂×#3964	C₂×C₃	1	2	yes	complemented
32	C₂×C₂²⋊#168	C₂×C₃	1	1	yes	characteristic, complemented
33	C₂⁴×C₃×C₅	—	2	8	no	—
34	C₂⁴×C₃×C₅	—	2	2	no	—
35	C₂⁴×C₃×C₅	—	2	4	no	—
36	C₂⁴×C₃×C₅	—	4	4	no	—
37	C₂⁴×C₃×C₅	—	4	4	no	—
38	C₂⁴×C₃×C₅	D₄	1	1	yes	characteristic
39	C₂³×C₃×D₅	—	2	1	no	—
40	C₂×C₃×C₅×D₄	—	2	8	no	—
41	C₂×C₃×C₅×D₄	—	2	16	no	—
42	C₂×C₃×C₅×D₄	—	2	16	no	—
43	C₂×C₃×C₅×D₄	—	2	2	no	—
44	C₂×C₃×C₅×D₄	—	2	4	no	—
45	C₂×C₃×C₅×D₄	—	2	4	no	—
46	C₂×C₃×C₅×D₄	D₄	1	8	yes	complemented
47	C₂×C₃×C₅×D₄	C₂³	1	4	yes	—
48	C₂²×C₃×C₄×C₅	—	2	4	no	—
49	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
50	C₂²×C₃×C₄×C₅	D₄	1	2	yes	—
51	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
52	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
53	C₂×C₃×C₂²⋊D₅	—	2	4	no	—
54	C₂×C₃×C₂²⋊D₅	—	4	4	no	—
55	C₂²×C₃×Dic₅	—	2	1	no	—
56	C₂×C₃×D₂₀	—	2	4	no	—
57	C₂×C₃×D₂₀	—	2	1	no	—
58	C₂×C₃×D₂₀	C₂³	1	2	yes	complemented
59	C₃×#686	—	2	16	no	—
60	C₃×#685	—	2	4	no	—
61	C₃×C₄⋊Dic₅	—	2	1	no	—
62	C₃×C₄⋊Dic₅	C₂³	1	2	yes	complemented
63	C₂×C₃×#168	—	2	4	no	—
64	C₂×C₃×#168	C₂³	1	4	yes	complemented
65	C₂³×C₃×D₄	D₅	1	1	yes	characteristic, complemented
66	C₂²×C₃×D₈	—	5	2	no	—
67	C₂×C₃×#121	—	5	1	no	—
68	C₃×#447	—	5	8	no	—
69	C₂×C₃×#102	—	5	2	no	—
70	C₂×C₃×C₂²⋊C₈	—	5	1	no	—
71	C₂⁵×C₅	—	2	1	no	—
72	C₂²×C₅×D₄	—	2	8	no	—
73	C₂²×C₅×D₄	—	2	1	no	—
74	C₂²×C₅×D₄	—	2	2	no	—
75	C₂²×C₅×D₄	C₂²×C₃	1	2	yes	—
76	C₂²×C₅×D₄	C₂²×C₃	1	4	yes	complemented
77	C₂³×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
78	C₂²×C₂²⋊D₅	—	2	1	no	—
79	C₂²×D₂₀	C₂²×C₃	1	1	yes	characteristic, complemented
80	C₂×#686	—	2	8	no	—
81	C₂×#686	C₂²×C₃	1	8	yes	complemented
82	#4076	—	2	2	no	—
83	#4076	C₂²×C₃	1	4	yes	complemented
84	C₂×#685	—	2	1	no	—
85	C₂×C₄⋊Dic₅	C₂²×C₃	1	1	yes	characteristic, complemented
86	C₂²×#168	C₂²×C₃	1	2	yes	complemented
87	#3964	C₂²×C₃	1	8	yes	complemented
88	C₂²⋊#168	C₂²×C₃	1	4	yes	complemented
89	C₂×#447	—	5	1	no	Sylow
90	C₂³×C₃×C₅	—	2	2	no	—
91	C₂³×C₃×C₅	—	2	2	no	—
92	C₂³×C₃×C₅	—	2	16	no	—
93	C₂³×C₃×C₅	—	2	8	no	—
94	C₂³×C₃×C₅	—	2	4	no	—
95	C₂³×C₃×C₅	—	4	8	no	—
96	C₂³×C₃×C₅	—	4	32	no	—
97	C₂³×C₃×C₅	—	4	4	no	—
98	C₂³×C₃×C₅	—	4	8	no	—
99	C₂³×C₃×C₅	—	4	4	no	—
100	C₂³×C₃×C₅	D₈	1	4	yes	complemented
101	C₂³×C₃×C₅	C₂×D₄	1	2	yes	—
102	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
103	C₂²×C₃×D₅	—	2	2	no	—
104	C₂²×C₃×D₅	—	4	2	no	—
105	C₂²×C₃×D₅	—	4	2	no	—
106	C₂²×C₃×D₅	—	4	2	no	—
107	C₃×C₅×D₄	—	2	16	no	—
108	C₃×C₅×D₄	—	2	8	no	—
109	C₃×C₅×D₄	—	2	4	no	—
110	C₃×C₅×D₄	C₂×D₄	1	8	yes	complemented
111	C₂×C₃×C₄×C₅	—	2	2	no	—
112	C₂×C₃×C₄×C₅	—	2	4	no	—
113	C₂×C₃×C₄×C₅	—	2	4	no	—
114	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
115	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
116	C₂×C₃×C₄×C₅	C₂×D₄	1	4	yes	—
117	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
118	C₃×C₂²⋊D₅	—	4	8	no	—
119	C₂×C₃×Dic₅	—	2	2	no	—
120	C₂×C₃×Dic₅	—	4	2	no	—
121	C₃×D₂₀	—	2	4	no	—
122	C₃×D₂₀	—	4	2	no	—
123	C₃×#168	—	2	4	no	—
124	C₂⁵×C₃	—	2	1	no	—
125	C₂²×C₃×D₄	—	2	8	no	—
126	C₂²×C₃×D₄	—	2	2	no	—
127	C₂²×C₃×D₄	—	2	1	no	—
128	C₂²×C₃×D₄	—	5	1	no	—
129	C₂²×C₃×D₄	—	10	1	no	—
130	C₂²×C₃×D₄	C₂×D₅	1	2	yes	—
131	C₂²×C₃×D₄	C₂×D₅	1	4	yes	complemented
132	C₂³×C₃×C₄	C₂×D₅	1	1	yes	characteristic
133	C₂×C₃×D₈	—	5	8	no	—
134	C₂×C₃×D₈	—	10	8	no	—
135	C₂²×C₃×C₈	—	5	2	no	—
136	C₃×#121	—	5	4	no	—
137	C₃×#121	—	10	2	no	—
138	C₂×C₃×C₄⋊C₄	—	5	1	no	—
139	C₂×C₃×C₂²⋊C₄	—	10	1	no	—
140	C₃×#102	—	5	8	no	—
141	C₃×C₂²⋊C₈	—	5	4	no	—
142	C₂⁴×C₅	—	2	8	no	—
143	C₂⁴×C₅	—	2	2	no	—
144	C₂⁴×C₅	—	2	4	no	—
145	C₂⁴×C₅	—	4	4	no	—
146	C₂⁴×C₅	—	4	4	no	—
147	C₂⁴×C₅	C₃×D₄	1	1	yes	characteristic
148	C₂³×D₅	—	2	1	no	—
149	C₂×C₅×D₄	—	2	8	no	—
150	C₂×C₅×D₄	—	2	16	no	—
151	C₂×C₅×D₄	—	2	16	no	—
152	C₂×C₅×D₄	—	2	2	no	—
153	C₂×C₅×D₄	—	2	4	no	—
154	C₂×C₅×D₄	—	2	4	no	—
155	C₂×C₅×D₄	C₃×D₄	1	8	yes	complemented
156	C₂×C₅×D₄	C₂³×C₃	1	4	yes	—
157	C₂²×C₄×C₅	—	2	4	no	—
158	C₂²×C₄×C₅	C₃×D₄	1	1	yes	characteristic
159	C₂²×C₄×C₅	C₃×D₄	1	2	yes	—
160	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
161	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
162	C₂×C₂²⋊D₅	—	2	4	no	—
163	C₂×C₂²⋊D₅	—	4	4	no	—
164	C₂²×Dic₅	—	2	1	no	—
165	C₂×D₂₀	—	2	4	no	—
166	C₂×D₂₀	—	2	1	no	—
167	C₂×D₂₀	C₂³×C₃	1	2	yes	complemented
168	#686	—	2	16	no	—
169	#685	—	2	4	no	—
170	C₄⋊Dic₅	—	2	1	no	—
171	C₄⋊Dic₅	C₂³×C₃	1	2	yes	complemented
172	C₂×#168	—	2	4	no	—
173	C₂×#168	C₂³×C₃	1	4	yes	complemented
174	C₂³×D₄	C₃×D₅	1	1	yes	characteristic, complemented
175	C₂²×D₈	—	5	2	no	—
176	C₂×#121	—	5	1	no	—
177	#447	—	5	8	no	—
178	C₂×#102	—	5	2	no	—
179	C₂×C₂²⋊C₈	—	5	1	no	—
180	C₂²×C₃×C₅	—	2	2	no	—
181	C₂²×C₃×C₅	—	2	2	no	—
182	C₂²×C₃×C₅	—	2	8	no	—
183	C₂²×C₃×C₅	—	2	8	no	—
184	C₂²×C₃×C₅	—	4	32	no	—
185	C₂²×C₃×C₅	—	4	4	no	—
186	C₂²×C₃×C₅	—	4	4	no	—
187	C₂²×C₃×C₅	—	4	16	no	—
188	C₂²×C₃×C₅	#120	1	2	yes	—
189	C₂²×C₃×C₅	C₂×D₈	1	2	yes	—
190	C₂²×C₃×C₅	C₂×D₈	1	4	yes	complemented
191	C₂²×C₃×C₅	AGL(1,ℤ/8)	1	2	yes	—
192	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
193	C₂×C₃×D₅	—	4	2	no	—
194	C₂×C₃×D₅	—	4	2	no	—
195	C₂×C₃×D₅	—	4	2	no	—
196	C₂×C₃×D₅	—	8	4	no	—
197	C₃×C₄×C₅	—	2	2	no	—
198	C₃×C₄×C₅	#120	1	2	yes	—
199	C₃×C₄×C₅	C₂²×D₄	1	2	yes	—
200	C₃×Dic₅	—	4	2	no	—
201	C₂⁴×C₃	—	2	8	no	—
202	C₂⁴×C₃	—	2	4	no	—
203	C₂⁴×C₃	—	2	2	no	—
204	C₂⁴×C₃	—	4	4	no	—
205	C₂⁴×C₃	—	4	4	no	—
206	C₂⁴×C₃	—	10	1	no	—
207	C₂⁴×C₃	C₂²⋊D₅	1	1	yes	characteristic
208	C₂×C₃×D₄	—	2	8	no	—
209	C₂×C₃×D₄	—	2	16	no	—
210	C₂×C₃×D₄	—	2	16	no	—
211	C₂×C₃×D₄	—	2	2	no	—
212	C₂×C₃×D₄	—	2	4	no	—
213	C₂×C₃×D₄	—	2	4	no	—
214	C₂×C₃×D₄	—	5	2	no	—
215	C₂×C₃×D₄	—	10	4	no	—
216	C₂×C₃×D₄	—	10	4	no	—
217	C₂×C₃×D₄	—	10	1	no	—
218	C₂×C₃×D₄	—	20	4	no	—
219	C₂×C₃×D₄	C₂²⋊D₅	1	8	yes	complemented
220	C₂×C₃×D₄	C₂²×D₅	1	4	yes	—
221	C₂²×C₃×C₄	—	2	4	no	—
222	C₂²×C₃×C₄	—	10	1	no	—
223	C₂²×C₃×C₄	C₂²⋊D₅	1	2	yes	—
224	C₂²×C₃×C₄	C₂²⋊D₅	1	1	yes	characteristic
225	C₂²×C₃×C₄	C₂²×D₅	1	2	yes	—
226	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
227	C₃×D₈	—	10	16	no	—
228	C₂×C₃×C₈	—	5	4	no	—
229	C₂×C₃×C₈	—	10	4	no	—
230	C₃×C₄⋊C₄	—	5	2	no	—
231	C₃×C₄⋊C₄	—	10	1	no	—
232	C₃×C₂²⋊C₄	—	10	4	no	—
233	C₂³×C₅	—	2	2	no	—
234	C₂³×C₅	—	2	2	no	—
235	C₂³×C₅	—	2	16	no	—
236	C₂³×C₅	—	2	8	no	—
237	C₂³×C₅	—	2	4	no	—
238	C₂³×C₅	—	4	8	no	—
239	C₂³×C₅	—	4	32	no	—
240	C₂³×C₅	—	4	4	no	—
241	C₂³×C₅	—	4	8	no	—
242	C₂³×C₅	—	4	4	no	—
243	C₂³×C₅	C₃×D₈	1	4	yes	complemented
244	C₂³×C₅	C₂×C₃×D₄	1	2	yes	—
245	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
246	C₂²×D₅	—	2	2	no	—
247	C₂²×D₅	—	4	2	no	—
248	C₂²×D₅	—	4	2	no	—
249	C₂²×D₅	—	4	2	no	—
250	C₅×D₄	—	2	16	no	—
251	C₅×D₄	—	2	8	no	—
252	C₅×D₄	—	2	4	no	—
253	C₅×D₄	C₂×C₃×D₄	1	8	yes	complemented
254	C₂×C₄×C₅	—	2	2	no	—
255	C₂×C₄×C₅	—	2	4	no	—
256	C₂×C₄×C₅	—	2	4	no	—
257	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
258	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
259	C₂×C₄×C₅	C₂×C₃×D₄	1	4	yes	—
260	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
261	C₂²⋊D₅	—	4	8	no	—
262	C₂×Dic₅	—	2	2	no	—
263	C₂×Dic₅	—	4	2	no	—
264	D₂₀	—	2	4	no	—
265	D₂₀	—	4	2	no	—
266	#168	—	2	4	no	—
267	C₂⁵	—	2	1	no	—
268	C₂²×D₄	—	2	8	no	—
269	C₂²×D₄	—	2	1	no	—
270	C₂²×D₄	—	2	2	no	—
271	C₂²×D₄	—	5	1	no	—
272	C₂²×D₄	—	10	1	no	—
273	C₂²×D₄	C₂×C₃×D₅	1	2	yes	—
274	C₂²×D₄	C₂×C₃×D₅	1	4	yes	complemented
275	C₂³×C₄	C₂×C₃×D₅	1	1	yes	characteristic
276	C₂×D₈	—	5	8	no	—
277	C₂×D₈	—	10	8	no	—
278	C₂²×C₈	—	5	2	no	—
279	#121	—	5	4	no	—
280	#121	—	10	2	no	—
281	C₂×C₄⋊C₄	—	5	1	no	—
282	C₂×C₂²⋊C₄	—	10	1	no	—
283	#102	—	5	8	no	—
284	C₂²⋊C₈	—	5	4	no	—
285	C₂×C₃×C₅	—	2	4	no	—
286	C₂×C₃×C₅	—	4	8	no	—
287	C₂×C₃×C₅	#447	1	4	yes	complemented
288	C₂×C₃×C₅	C₂×#120	1	1	yes	characteristic
289	C₂×C₃×C₅	C₂²×D₈	1	1	yes	characteristic
290	C₂×C₃×C₅	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
291	C₃×D₅	—	8	2	no	—
292	C₂³×C₃	—	2	2	no	—
293	C₂³×C₃	—	2	2	no	—
294	C₂³×C₃	—	2	16	no	—
295	C₂³×C₃	—	2	8	no	—
296	C₂³×C₃	—	2	4	no	—
297	C₂³×C₃	—	4	8	no	—
298	C₂³×C₃	—	4	32	no	—
299	C₂³×C₃	—	4	4	no	—
300	C₂³×C₃	—	4	8	no	—
301	C₂³×C₃	—	4	4	no	—
302	C₂³×C₃	—	10	2	no	—
303	C₂³×C₃	—	20	2	no	—
304	C₂³×C₃	—	20	2	no	—
305	C₂³×C₃	—	20	2	no	—
306	C₂³×C₃	#686	1	4	yes	complemented
307	C₂³×C₃	C₂×C₂²⋊D₅	1	2	yes	—
308	C₂³×C₃	C₂×C₂²⋊D₅	1	1	yes	characteristic
309	C₃×D₄	—	2	16	no	—
310	C₃×D₄	—	2	8	no	—
311	C₃×D₄	—	2	4	no	—
312	C₃×D₄	—	10	4	no	—
313	C₃×D₄	—	20	8	no	—
314	C₃×D₄	—	20	2	no	—
315	C₃×D₄	C₂×C₂²⋊D₅	1	8	yes	complemented
316	C₂×C₃×C₄	—	2	2	no	—
317	C₂×C₃×C₄	—	2	4	no	—
318	C₂×C₃×C₄	—	2	4	no	—
319	C₂×C₃×C₄	—	10	2	no	—
320	C₂×C₃×C₄	—	20	2	no	—
321	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	2	yes	—
322	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	1	yes	characteristic
323	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	4	yes	—
324	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
325	C₃×C₈	—	10	4	no	—
326	C₂²×C₅	—	2	2	no	—
327	C₂²×C₅	—	2	8	no	—
328	C₂²×C₅	—	2	2	no	—
329	C₂²×C₅	—	2	8	no	—
330	C₂²×C₅	—	4	32	no	—
331	C₂²×C₅	—	4	4	no	—
332	C₂²×C₅	—	4	4	no	—
333	C₂²×C₅	—	4	16	no	—
334	C₂²×C₅	C₃×#120	1	2	yes	—
335	C₂²×C₅	C₂×C₃×D₈	1	2	yes	—
336	C₂²×C₅	C₂×C₃×D₈	1	4	yes	complemented
337	C₂²×C₅	C₃×AGL(1,ℤ/8)	1	2	yes	—
338	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
339	C₂×D₅	—	4	2	no	—
340	C₂×D₅	—	4	2	no	—
341	C₂×D₅	—	4	2	no	—
342	C₂×D₅	—	8	4	no	—
343	C₄×C₅	—	2	2	no	—
344	C₄×C₅	C₃×#120	1	2	yes	—
345	C₄×C₅	C₂²×C₃×D₄	1	2	yes	—
346	Dic₅	—	4	2	no	—
347	C₂⁴	—	2	8	no	—
348	C₂⁴	—	2	2	no	—
349	C₂⁴	—	2	4	no	—
350	C₂⁴	—	4	4	no	—
351	C₂⁴	—	4	4	no	—
352	C₂⁴	—	10	1	no	—
353	C₂⁴	C₃×C₂²⋊D₅	1	1	yes	characteristic
354	C₂×D₄	—	2	8	no	—
355	C₂×D₄	—	2	16	no	—
356	C₂×D₄	—	2	16	no	—
357	C₂×D₄	—	2	2	no	—
358	C₂×D₄	—	2	4	no	—
359	C₂×D₄	—	2	4	no	—
360	C₂×D₄	—	5	2	no	—
361	C₂×D₄	—	10	4	no	—
362	C₂×D₄	—	10	4	no	—
363	C₂×D₄	—	10	1	no	—
364	C₂×D₄	—	20	4	no	—
365	C₂×D₄	C₃×C₂²⋊D₅	1	8	yes	complemented
366	C₂×D₄	C₂²×C₃×D₅	1	4	yes	—
367	C₂²×C₄	—	2	4	no	—
368	C₂²×C₄	—	10	1	no	—
369	C₂²×C₄	C₃×C₂²⋊D₅	1	1	yes	characteristic
370	C₂²×C₄	C₃×C₂²⋊D₅	1	2	yes	—
371	C₂²×C₄	C₂²×C₃×D₅	1	2	yes	—
372	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
373	D₈	—	10	16	no	—
374	C₂×C₈	—	5	4	no	—
375	C₂×C₈	—	10	4	no	—
376	C₄⋊C₄	—	5	2	no	—
377	C₄⋊C₄	—	10	1	no	—
378	C₂²⋊C₄	—	10	4	no	—
379	C₃×C₅	C₂×#447	1	1	yes	characteristic, complemented, Hall
380	C₂²×C₃	—	2	2	no	—
381	C₂²×C₃	—	2	2	no	—
382	C₂²×C₃	—	2	8	no	—
383	C₂²×C₃	—	2	8	no	—
384	C₂²×C₃	—	4	32	no	—
385	C₂²×C₃	—	4	4	no	—
386	C₂²×C₃	—	4	4	no	—
387	C₂²×C₃	—	4	16	no	—
388	C₂²×C₃	—	20	2	no	—
389	C₂²×C₃	—	20	2	no	—
390	C₂²×C₃	—	20	2	no	—
391	C₂²×C₃	—	40	4	no	—
392	C₂²×C₃	C₂×#686	1	2	yes	—
393	C₂²×C₃	C₂×#686	1	4	yes	complemented
394	C₂²×C₃	#4078	1	2	yes	—
395	C₂²×C₃	#4099	1	2	yes	—
396	C₂²×C₃	C₂²×C₂²⋊D₅	1	1	yes	characteristic
397	C₃×C₄	—	2	2	no	—
398	C₃×C₄	—	20	2	no	—
399	C₃×C₄	#4099	1	2	yes	—
400	C₃×C₄	C₂²×C₂²⋊D₅	1	2	yes	—
401	C₂×C₅	—	2	4	no	—
402	C₂×C₅	—	4	8	no	—
403	C₂×C₅	C₃×#447	1	4	yes	complemented
404	C₂×C₅	C₂×C₃×#120	1	1	yes	characteristic
405	C₂×C₅	C₂²×C₃×D₈	1	1	yes	characteristic
406	C₂×C₅	C₂×C₃×AGL(1,ℤ/8)	1	1	yes	characteristic
407	D₅	—	8	2	no	—
408	C₂³	—	2	2	no	—
409	C₂³	—	2	2	no	—
410	C₂³	—	2	16	no	—
411	C₂³	—	2	8	no	—
412	C₂³	—	2	4	no	—
413	C₂³	—	4	8	no	—
414	C₂³	—	4	32	no	—
415	C₂³	—	4	4	no	—
416	C₂³	—	4	8	no	—
417	C₂³	—	4	4	no	—
418	C₂³	—	10	2	no	—
419	C₂³	—	20	2	no	—
420	C₂³	—	20	2	no	—
421	C₂³	—	20	2	no	—
422	C₂³	C₃×#686	1	4	yes	complemented
423	C₂³	C₂×C₃×C₂²⋊D₅	1	2	yes	—
424	C₂³	C₂×C₃×C₂²⋊D₅	1	1	yes	characteristic
425	D₄	—	2	16	no	—
426	D₄	—	2	8	no	—
427	D₄	—	2	4	no	—
428	D₄	—	10	4	no	—
429	D₄	—	20	8	no	—
430	D₄	—	20	2	no	—
431	D₄	C₂×C₃×C₂²⋊D₅	1	8	yes	complemented
432	C₂×C₄	—	2	2	no	—
433	C₂×C₄	—	2	4	no	—
434	C₂×C₄	—	2	4	no	—
435	C₂×C₄	—	10	2	no	—
436	C₂×C₄	—	20	2	no	—
437	C₂×C₄	C₂×C₃×C₂²⋊D₅	1	2	yes	—
438	C₂×C₄	C₂×C₃×C₂²⋊D₅	1	1	yes	characteristic
439	C₂×C₄	C₂×C₃×C₂²⋊D₅	1	4	yes	—
440	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
441	C₈	—	10	4	no	—
442	C₂×C₃	—	2	4	no	—
443	C₂×C₃	—	4	8	no	—
444	C₂×C₃	—	40	2	no	—
445	C₂×C₃	#65506	1	4	yes	direct product factor
446	C₂×C₃	C₂²×#686	1	1	yes	characteristic
447	C₂×C₃	C₂×#4078	1	1	yes	characteristic
448	C₂×C₃	C₂×#4099	1	1	yes	characteristic
449	C₅	C₂×C₃×#447	1	1	yes	characteristic, complemented, Sylow
450	C₂²	—	2	2	no	—
451	C₂²	—	2	2	no	—
452	C₂²	—	2	8	no	—
453	C₂²	—	2	8	no	—
454	C₂²	—	4	32	no	—
455	C₂²	—	4	4	no	—
456	C₂²	—	4	4	no	—
457	C₂²	—	4	16	no	—
458	C₂²	—	20	2	no	—
459	C₂²	—	20	2	no	—
460	C₂²	—	20	2	no	—
461	C₂²	—	40	4	no	—
462	C₂²	C₂×C₃×#686	1	2	yes	—
463	C₂²	C₂×C₃×#686	1	4	yes	complemented
464	C₂²	C₃×#4078	1	2	yes	—
465	C₂²	C₃×#4099	1	2	yes	—
466	C₂²	C₂²×C₃×C₂²⋊D₅	1	1	yes	characteristic
467	C₄	—	2	2	no	—
468	C₄	—	20	2	no	—
469	C₄	C₃×#4099	1	2	yes	—
470	C₄	C₂²×C₃×C₂²⋊D₅	1	2	yes	—
471	C₃	C₂×#65506	1	1	yes	characteristic, direct product factor, Sylow
472	C₂	—	2	4	no	—
473	C₂	—	4	8	no	—
474	C₂	—	40	2	no	—
475	C₂	C₃×#65506	1	4	yes	direct product factor
476	C₂	C₂²×C₃×#686	1	1	yes	characteristic
477	C₂	C₂×C₃×#4078	1	1	yes	characteristic
478	C₂	C₂×C₃×#4099	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₃	C₂×C₂²⋊D₅
commutator, cosocle	C₂×C₄×C₅	C₂⁴×C₃
Frattini	C₂×C₄	C₂³×C₃×D₅
Fitting	C₂³×C₃×C₅×D₄	C₂
socle	C₂³×C₃×C₅	C₂×D₄
hypercenter	C₂³×C₃×D₄	D₅
hypocenter	C₅	C₂×C₃×#447
LCS	G ▷ C₂×C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂³×C₃ ◁ C₂³×C₃×C₄ ◁ C₂³×C₃×D₄

Complements

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

N	H ≅ G/N	type
1. C₂³×C₃×C₅×D₄	C₂	semidirect
2. C₂²×C₃×#686	C₂	semidirect
3. C₂×C₃×#4076	C₂	semidirect
4. C₃×#65506	C₂	direct (N × H)
5. C₂×C₃×#3964	C₂	semidirect
6. C₂×C₃×C₂²⋊#168	C₂	semidirect
7. C₂×#65506	C₃	direct (N × H)
13. C₂²×C₃×C₅×D₄	C₂²	semidirect
16. C₂²×C₃×D₂₀	C₂²	semidirect
18. C₂×C₃×#686	C₂²	semidirect
20. C₃×#4076	C₂²	semidirect
22. C₂×C₃×C₄⋊Dic₅	C₂²	semidirect
23. C₂²×C₃×#168	C₂²	semidirect
24. C₃×#3964	C₂²	semidirect
25. C₃×C₂²⋊#168	C₂²	semidirect
27. C₂³×C₅×D₄	C₂×C₃	semidirect
28. C₂²×#686	C₂×C₃	semidirect
29. C₂×#4076	C₂×C₃	semidirect
30. #65506	C₂×C₃	direct (N × H)
31. C₂×#3964	C₂×C₃	semidirect
32. C₂×C₂²⋊#168	C₂×C₃	semidirect
46. C₂×C₃×C₅×D₄	D₄	semidirect
58. C₂×C₃×D₂₀	C₂³	semidirect
62. C₃×C₄⋊Dic₅	C₂³	semidirect
64. C₂×C₃×#168	C₂³	semidirect
65. C₂³×C₃×D₄	D₅	semidirect
76. C₂²×C₅×D₄	C₂²×C₃	semidirect
79. C₂²×D₂₀	C₂²×C₃	semidirect
81. C₂×#686	C₂²×C₃	semidirect
83. #4076	C₂²×C₃	semidirect
85. C₂×C₄⋊Dic₅	C₂²×C₃	semidirect
86. C₂²×#168	C₂²×C₃	semidirect
87. #3964	C₂²×C₃	semidirect
88. C₂²⋊#168	C₂²×C₃	semidirect
100. C₂³×C₃×C₅	D₈	semidirect
110. C₃×C₅×D₄	C₂×D₄	semidirect
131. C₂²×C₃×D₄	C₂×D₅	semidirect
155. C₂×C₅×D₄	C₃×D₄	semidirect
167. C₂×D₂₀	C₂³×C₃	semidirect
171. C₄⋊Dic₅	C₂³×C₃	semidirect
173. C₂×#168	C₂³×C₃	semidirect
174. C₂³×D₄	C₃×D₅	semidirect
190. C₂²×C₃×C₅	C₂×D₈	semidirect
219. C₂×C₃×D₄	C₂²⋊D₅	semidirect
243. C₂³×C₅	C₃×D₈	semidirect
253. C₅×D₄	C₂×C₃×D₄	semidirect
274. C₂²×D₄	C₂×C₃×D₅	semidirect
287. C₂×C₃×C₅	#447	semidirect
306. C₂³×C₃	#686	semidirect
315. C₃×D₄	C₂×C₂²⋊D₅	semidirect
336. C₂²×C₅	C₂×C₃×D₈	semidirect
365. C₂×D₄	C₃×C₂²⋊D₅	semidirect
379. C₃×C₅	C₂×#447	semidirect
393. C₂²×C₃	C₂×#686	semidirect
403. C₂×C₅	C₃×#447	semidirect
422. C₂³	C₃×#686	semidirect
431. D₄	C₂×C₃×C₂²⋊D₅	semidirect
445. C₂×C₃	#65506	direct (N × H)
449. C₅	C₂×C₃×#447	semidirect
463. C₂²	C₂×C₃×#686	semidirect
471. C₃	C₂×#65506	direct (N × H)
475. C₂	C₃×#65506	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×C₃×C₅×D₄	2
C₂²×C₃×#686	2
C₂×C₃×#4076	2
C₃×#65506	2
C₂×C₃×#3964	2
C₂×C₃×C₂²⋊#168	2
C₂×#65506	3
C₂×C₃×#447	5

Subgroups — C2×C3×#65506 #14423182

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#65506 #14423182