Subgroups — C₃×C₄×#4065 #14416216

Order 1920.

1000 conjugacy classes of subgroups.

The subgroup lattice has 496 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#4065	C₂	1	1	yes	maximal, characteristic
2	C₃×C₄×#713	C₂	1	2	yes	maximal, complemented
3	C₃×C₄×C₅×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×Q₁₆×Dic₅	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×C₄×#688	C₂	1	2	yes	maximal, complemented
6	C₃×#65169	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#65161	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#65093	C₂	1	2	yes	maximal, complemented
9	C₃×#65077	C₂	1	2	yes	maximal, complemented
10	C₃×C₄×D₄₀	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×C₄×C₈×D₅	C₂	1	1	yes	maximal, characteristic, complemented
12	C₄×#4065	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂×C₃×#713	C₂²	1	2	yes	—
14	C₂×C₃×C₅×Q₁₆	C₂²	1	1	yes	characteristic
15	C₃×C₄×C₅×Q₈	C₂²	1	2	yes	—
16	C₃×Q₈×Dic₅	C₂²	1	2	yes	—
17	C₂×C₃×#688	C₂²	1	2	yes	—
18	C₃×#4065	C₄	1	8	yes	direct product factor
19	C₂×C₃×D₄₀	C₂²	1	1	yes	characteristic
20	C₂×C₃×C₈×D₅	C₂²	1	1	yes	characteristic
21	C₂×C₃×C₈×D₅	C₂²	1	1	yes	characteristic
22	C₃×#4039	—	2	2	no	—
23	C₃×#4039	C₂²	1	2	yes	—
24	C₃×#4038	—	2	2	no	—
25	C₃×#4038	C₂²	1	2	yes	—
26	C₃×C₄×D₂₀	—	2	2	no	—
27	C₃×C₄×D₂₀	C₂²	1	2	yes	—
28	C₃×C₄²×D₅	—	2	2	no	—
29	C₃×C₄²×D₅	C₂²	1	1	yes	characteristic
30	C₃×C₅×#107	C₂²	1	1	yes	characteristic
31	C₃×C₅×#103	C₂²	1	2	yes	—
32	C₃×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
33	C₃×#3967	C₂²	1	2	yes	—
34	C₃×#3953	C₂²	1	2	yes	—
35	C₃×#3950	C₂²	1	1	yes	characteristic
36	C₃×C₈×Dic₅	C₂²	1	1	yes	characteristic
37	C₃×C₈×Dic₅	C₂²	1	1	yes	characteristic
38	C₃×#3941	C₂²	1	2	yes	—
39	C₃×#3940	C₂²	1	2	yes	—
40	C₃×C₄×#168	C₂²	1	1	yes	characteristic
41	C₃×C₄×#135	—	5	1	no	maximal, Hall
42	C₂×#4065	C₂×C₃	1	1	yes	characteristic
43	C₄×#713	C₂×C₃	1	2	yes	complemented
44	C₄×C₅×Q₁₆	C₂×C₃	1	1	yes	characteristic, complemented
45	Q₁₆×Dic₅	C₂×C₃	1	1	yes	characteristic, complemented
46	C₄×#688	C₂×C₃	1	2	yes	complemented
47	#65169	C₂×C₃	1	1	yes	characteristic, complemented
48	#65161	C₂×C₃	1	1	yes	characteristic, complemented
49	#65093	C₂×C₃	1	2	yes	complemented
50	#65077	C₂×C₃	1	2	yes	complemented
51	C₄×D₄₀	C₂×C₃	1	1	yes	characteristic, complemented
52	C₄×C₈×D₅	C₂×C₃	1	1	yes	characteristic, complemented
53	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
54	C₃×#713	—	2	4	no	—
55	C₃×#713	C₂×C₄	1	8	yes	complemented
56	C₂×C₃×D₂₀	—	2	2	no	—
57	C₂×C₃×D₂₀	C₂³	1	2	yes	—
58	C₂×C₃×C₄×D₅	—	2	2	no	—
59	C₂×C₃×C₄×D₅	—	2	2	no	—
60	C₂×C₃×C₄×D₅	—	2	2	no	—
61	C₂×C₃×C₄×D₅	D₄	1	1	yes	characteristic
62	C₂×C₃×C₄×D₅	D₄	1	1	yes	characteristic
63	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
64	C₃×C₅×Q₁₆	C₂×C₄	1	4	yes	complemented
65	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
66	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
67	C₃×C₅×C₄⋊C₄	—	2	2	no	—
68	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
69	C₃×C₄²×C₅	—	2	2	no	—
70	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
71	C₃×#688	C₂×C₄	1	8	yes	complemented
72	C₃×#685	—	2	2	no	—
73	C₃×#685	—	2	2	no	—
74	C₃×#685	—	2	2	no	—
75	C₃×C₄⋊Dic₅	—	2	2	no	—
76	C₃×C₄⋊Dic₅	C₂³	1	2	yes	—
77	C₃×C₄×Dic₅	—	2	2	no	—
78	C₃×C₄×Dic₅	—	2	2	no	—
79	C₃×C₄×Dic₅	D₄	1	1	yes	characteristic
80	C₃×C₄×Dic₅	D₄	1	1	yes	characteristic
81	C₃×C₄×Dic₅	C₂³	1	1	yes	characteristic
82	C₂×C₃×#168	C₂³	1	1	yes	characteristic
83	C₂×C₃×#168	C₂³	1	1	yes	characteristic
84	C₃×D₄₀	C₂×C₄	1	4	yes	complemented
85	C₃×C₈×D₅	—	2	2	no	—
86	C₃×C₈×D₅	C₂×C₄	1	4	yes	complemented
87	C₂×C₃×#135	—	5	1	no	—
88	C₃×C₄×#41	—	5	2	no	—
89	C₃×C₄×Q₁₆	—	5	1	no	—
90	C₃×C₄×Q₁₆	D₅	1	1	yes	characteristic, complemented
91	C₃×C₄×SD₁₆	—	5	2	no	—
92	C₃×C₄×SD₁₆	—	5	2	no	—
93	C₃×C₄×D₈	—	5	1	no	—
94	C₃×C₄×D₈	—	5	1	no	—
95	C₃×#427	—	5	1	no	—
96	C₃×#416	—	5	2	no	—
97	C₂×C₃×C₄×C₈	—	5	1	no	—
98	C₂×#713	C₂²×C₃	1	2	yes	—
99	C₂×C₅×Q₁₆	C₂²×C₃	1	1	yes	characteristic
100	C₄×C₅×Q₈	C₂²×C₃	1	2	yes	—
101	Q₈×Dic₅	C₂²×C₃	1	2	yes	—
102	C₂×#688	C₂²×C₃	1	2	yes	—
103	#4065	C₃×C₄	1	8	yes	direct product factor
104	C₂×D₄₀	C₂²×C₃	1	1	yes	characteristic
105	C₂×C₈×D₅	C₂²×C₃	1	1	yes	characteristic
106	C₂×C₈×D₅	C₂²×C₃	1	1	yes	characteristic
107	#4039	—	2	2	no	—
108	#4039	C₂²×C₃	1	2	yes	—
109	#4038	—	2	2	no	—
110	#4038	C₂²×C₃	1	2	yes	—
111	C₄×D₂₀	—	2	2	no	—
112	C₄×D₂₀	C₂²×C₃	1	2	yes	—
113	C₄²×D₅	—	2	2	no	—
114	C₄²×D₅	C₂²×C₃	1	1	yes	characteristic
115	C₅×#107	C₂²×C₃	1	1	yes	characteristic
116	C₅×#103	C₂²×C₃	1	2	yes	—
117	C₄×C₅×C₈	C₂²×C₃	1	1	yes	characteristic
118	#3967	C₂²×C₃	1	2	yes	—
119	#3953	C₂²×C₃	1	2	yes	—
120	#3950	C₂²×C₃	1	1	yes	characteristic
121	C₈×Dic₅	C₂²×C₃	1	1	yes	characteristic
122	C₈×Dic₅	C₂²×C₃	1	1	yes	characteristic
123	#3941	C₂²×C₃	1	2	yes	—
124	#3940	C₂²×C₃	1	2	yes	—
125	C₄×#168	C₂²×C₃	1	1	yes	characteristic
126	C₄×#135	—	5	1	no	Sylow
127	C₂²×C₃×D₅	—	2	2	no	—
128	C₂²×C₃×D₅	C₂×D₄	1	1	yes	characteristic
129	C₃×C₅×Q₈	—	2	2	no	—
130	C₃×C₅×Q₈	C₂²×C₄	1	4	yes	—
131	C₂×C₃×C₄×C₅	—	2	2	no	—
132	C₂×C₃×C₄×C₅	—	2	2	no	—
133	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
134	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
135	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
136	C₂×C₃×Dic₅	—	2	2	no	—
137	C₂×C₃×Dic₅	C₂×D₄	1	1	yes	characteristic
138	C₂×C₃×Dic₅	C₂×D₄	1	1	yes	characteristic
139	C₂×C₃×Dic₅	C₂×D₄	1	1	yes	characteristic
140	C₃×D₂₀	—	2	8	no	—
141	C₃×D₂₀	—	2	2	no	—
142	C₃×D₂₀	C₂²×C₄	1	4	yes	—
143	C₃×C₄×D₅	—	2	2	no	—
144	C₃×C₄×D₅	—	2	8	no	—
145	C₃×C₄×D₅	—	2	2	no	—
146	C₃×C₄×D₅	—	4	4	no	—
147	C₃×C₄×D₅	—	4	4	no	—
148	C₃×C₄×D₅	C₂²×C₄	1	2	yes	—
149	C₃×C₄×D₅	#41	1	2	yes	—
150	C₃×C₅×C₈	—	2	1	no	—
151	C₃×C₅×C₈	C₂²×C₄	1	2	yes	—
152	C₃×#168	—	2	1	no	—
153	C₃×#168	C₂²×C₄	1	2	yes	—
154	C₂×C₃×#41	—	5	2	no	—
155	C₃×#135	—	5	8	no	—
156	C₂×C₃×Q₁₆	C₂×D₅	1	1	yes	characteristic
157	C₂×C₃×SD₁₆	—	5	2	no	—
158	C₂×C₃×D₈	—	5	1	no	—
159	C₂²×C₃×C₈	—	5	1	no	—
160	C₂²×C₃×C₈	—	5	1	no	—
161	C₃×C₄×Q₈	—	5	2	no	—
162	C₃×C₄×Q₈	C₂×D₅	1	2	yes	—
163	C₃×C₄×D₄	—	5	2	no	—
164	C₃×C₄×D₄	—	5	2	no	—
165	C₃×C₄×D₄	—	10	2	no	—
166	C₃×C₄×D₄	—	10	2	no	—
167	C₃×#117	—	5	2	no	—
168	C₃×#117	—	10	2	no	—
169	C₂×C₃×C₄²	—	5	1	no	—
170	C₂×C₃×C₄²	—	10	2	no	—
171	C₃×#107	—	5	1	no	—
172	C₃×#107	C₂×D₅	1	1	yes	characteristic
173	C₃×#106	—	5	2	no	—
174	C₃×#103	—	5	2	no	—
175	C₃×#103	C₂×D₅	1	2	yes	—
176	C₃×#102	—	5	2	no	—
177	C₃×#102	—	5	2	no	—
178	C₃×C₄×C₈	—	5	1	no	—
179	C₃×C₄×C₈	—	5	1	no	—
180	C₃×C₄×C₈	—	5	1	no	—
181	C₃×C₄×C₈	C₂×D₅	1	1	yes	characteristic
182	C₂×C₅×Q₈	C₂³×C₃	1	2	yes	—
183	#713	—	2	4	no	—
184	#713	C₂×C₃×C₄	1	8	yes	complemented
185	C₂×D₂₀	—	2	2	no	—
186	C₂×D₂₀	C₂³×C₃	1	2	yes	—
187	C₂×C₄×D₅	—	2	2	no	—
188	C₂×C₄×D₅	—	2	2	no	—
189	C₂×C₄×D₅	—	2	2	no	—
190	C₂×C₄×D₅	C₃×D₄	1	1	yes	characteristic
191	C₂×C₄×D₅	C₃×D₄	1	1	yes	characteristic
192	C₂×C₄×D₅	C₂³×C₃	1	1	yes	characteristic
193	C₅×Q₁₆	C₂×C₃×C₄	1	4	yes	complemented
194	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
195	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
196	C₅×C₄⋊C₄	—	2	2	no	—
197	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
198	C₄²×C₅	—	2	2	no	—
199	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
200	#688	C₂×C₃×C₄	1	8	yes	complemented
201	#685	—	2	2	no	—
202	#685	—	2	2	no	—
203	#685	—	2	2	no	—
204	C₄⋊Dic₅	—	2	2	no	—
205	C₄⋊Dic₅	C₂³×C₃	1	2	yes	—
206	C₄×Dic₅	—	2	2	no	—
207	C₄×Dic₅	—	2	2	no	—
208	C₄×Dic₅	C₃×D₄	1	1	yes	characteristic
209	C₄×Dic₅	C₃×D₄	1	1	yes	characteristic
210	C₄×Dic₅	C₂³×C₃	1	1	yes	characteristic
211	C₂×#168	C₂³×C₃	1	1	yes	characteristic
212	C₂×#168	C₂³×C₃	1	1	yes	characteristic
213	D₄₀	C₂×C₃×C₄	1	4	yes	complemented
214	C₈×D₅	—	2	2	no	—
215	C₈×D₅	C₂×C₃×C₄	1	4	yes	complemented
216	C₂×#135	—	5	1	no	—
217	C₄×#41	—	5	2	no	—
218	C₄×Q₁₆	—	5	1	no	—
219	C₄×Q₁₆	C₃×D₅	1	1	yes	characteristic, complemented
220	C₄×SD₁₆	—	5	2	no	—
221	C₄×SD₁₆	—	5	2	no	—
222	C₄×D₈	—	5	1	no	—
223	C₄×D₈	—	5	1	no	—
224	#427	—	5	1	no	—
225	#416	—	5	2	no	—
226	C₂×C₄×C₈	—	5	1	no	—
227	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
228	C₂×C₃×D₅	—	2	1	no	—
229	C₂×C₃×D₅	—	2	1	no	—
230	C₂×C₃×D₅	—	2	4	no	—
231	C₂×C₃×D₅	—	4	2	no	—
232	C₂×C₃×D₅	—	4	2	no	—
233	C₂×C₃×D₅	C₄×D₄	1	2	yes	—
234	C₃×C₄×C₅	—	2	4	no	—
235	C₃×C₄×C₅	—	2	1	no	—
236	C₃×C₄×C₅	—	4	2	no	—
237	C₃×C₄×C₅	#135	1	2	yes	complemented
238	C₃×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
239	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
240	C₃×Dic₅	—	2	1	no	—
241	C₃×Dic₅	—	4	2	no	—
242	C₃×Dic₅	C₄×D₄	1	2	yes	—
243	C₃×Dic₅	#135	1	2	yes	complemented
244	C₃×#41	—	5	8	no	—
245	C₃×#41	—	10	4	no	—
246	C₂×C₃×Q₈	C₂²×D₅	1	2	yes	—
247	C₂×C₃×D₄	—	5	2	no	—
248	C₂×C₃×D₄	—	10	2	no	—
249	C₂²×C₃×C₄	—	5	1	no	—
250	C₂²×C₃×C₄	—	5	1	no	—
251	C₂²×C₃×C₄	—	5	1	no	—
252	C₂²×C₃×C₄	—	10	2	no	—
253	C₂²×C₃×C₄	—	10	2	no	—
254	C₂²×C₃×C₄	—	10	2	no	—
255	C₃×Q₁₆	C₄×D₅	1	4	yes	complemented
256	C₃×SD₁₆	—	5	8	no	—
257	C₃×D₈	—	5	4	no	—
258	C₂×C₃×C₈	—	5	1	no	—
259	C₂×C₃×C₈	—	5	4	no	—
260	C₂×C₃×C₈	—	5	1	no	—
261	C₂×C₃×C₈	—	10	2	no	—
262	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
263	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
264	C₃×C₄⋊C₄	—	2	2	no	—
265	C₃×C₄⋊C₄	—	5	2	no	—
266	C₃×C₄⋊C₄	—	10	2	no	—
267	C₃×C₄⋊C₄	C₂²×D₅	1	2	yes	—
268	C₃×C₂²⋊C₄	—	10	2	no	—
269	C₃×C₂²⋊C₄	—	10	2	no	—
270	C₃×C₂²⋊C₄	—	10	2	no	—
271	C₃×C₄²	—	2	2	no	—
272	C₃×C₄²	—	5	1	no	—
273	C₃×C₄²	—	5	1	no	—
274	C₃×C₄²	—	5	1	no	—
275	C₃×C₄²	—	10	2	no	—
276	C₃×C₄²	—	10	2	no	—
277	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
278	C₂²×D₅	—	2	2	no	—
279	C₂²×D₅	C₂×C₃×D₄	1	1	yes	characteristic
280	C₅×Q₈	—	2	2	no	—
281	C₅×Q₈	C₂²×C₃×C₄	1	4	yes	—
282	C₂×C₄×C₅	—	2	2	no	—
283	C₂×C₄×C₅	—	2	2	no	—
284	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
285	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
286	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
287	C₂×Dic₅	—	2	2	no	—
288	C₂×Dic₅	C₂×C₃×D₄	1	1	yes	characteristic
289	C₂×Dic₅	C₂×C₃×D₄	1	1	yes	characteristic
290	C₂×Dic₅	C₂×C₃×D₄	1	1	yes	characteristic
291	D₂₀	—	2	8	no	—
292	D₂₀	—	2	2	no	—
293	D₂₀	C₂²×C₃×C₄	1	4	yes	—
294	C₄×D₅	—	2	2	no	—
295	C₄×D₅	—	2	8	no	—
296	C₄×D₅	—	2	2	no	—
297	C₄×D₅	—	4	4	no	—
298	C₄×D₅	—	4	4	no	—
299	C₄×D₅	C₂²×C₃×C₄	1	2	yes	—
300	C₄×D₅	C₃×#41	1	2	yes	—
301	C₅×C₈	—	2	1	no	—
302	C₅×C₈	C₂²×C₃×C₄	1	2	yes	—
303	#168	—	2	1	no	—
304	#168	C₂²×C₃×C₄	1	2	yes	—
305	C₂×#41	—	5	2	no	—
306	#135	—	5	8	no	—
307	C₂×Q₁₆	C₂×C₃×D₅	1	1	yes	characteristic
308	C₂×SD₁₆	—	5	2	no	—
309	C₂×D₈	—	5	1	no	—
310	C₂²×C₈	—	5	1	no	—
311	C₂²×C₈	—	5	1	no	—
312	C₄×Q₈	—	5	2	no	—
313	C₄×Q₈	C₂×C₃×D₅	1	2	yes	—
314	C₄×D₄	—	5	2	no	—
315	C₄×D₄	—	5	2	no	—
316	C₄×D₄	—	10	2	no	—
317	C₄×D₄	—	10	2	no	—
318	#117	—	5	2	no	—
319	#117	—	10	2	no	—
320	C₂×C₄²	—	5	1	no	—
321	C₂×C₄²	—	10	2	no	—
322	#107	—	5	1	no	—
323	#107	C₂×C₃×D₅	1	1	yes	characteristic
324	#106	—	5	2	no	—
325	#103	—	5	2	no	—
326	#103	C₂×C₃×D₅	1	2	yes	—
327	#102	—	5	2	no	—
328	#102	—	5	2	no	—
329	C₄×C₈	—	5	1	no	—
330	C₄×C₈	—	5	1	no	—
331	C₄×C₈	—	5	1	no	—
332	C₄×C₈	C₂×C₃×D₅	1	1	yes	characteristic
333	C₂×C₃×C₅	C₂×C₄×D₄	1	1	yes	characteristic
334	C₂×C₃×C₅	C₂×#135	1	1	yes	characteristic
335	C₂×C₃×C₅	C₂×#135	1	1	yes	characteristic
336	C₃×D₅	—	2	2	no	—
337	C₃×D₅	—	4	4	no	—
338	C₂³×C₃	—	5	1	no	—
339	C₂³×C₃	—	10	2	no	—
340	C₃×Q₈	—	2	2	no	—
341	C₃×Q₈	C₂×C₄×D₅	1	4	yes	—
342	C₃×D₄	—	5	4	no	—
343	C₃×D₄	—	10	8	no	—
344	C₃×D₄	—	10	2	no	—
345	C₂×C₃×C₄	—	2	2	no	—
346	C₂×C₃×C₄	—	2	2	no	—
347	C₂×C₃×C₄	—	5	1	no	—
348	C₂×C₃×C₄	—	5	1	no	—
349	C₂×C₃×C₄	—	5	2	no	—
350	C₂×C₃×C₄	—	5	2	no	—
351	C₂×C₃×C₄	—	5	1	no	—
352	C₂×C₃×C₄	—	10	2	no	—
353	C₂×C₃×C₄	—	10	8	no	—
354	C₂×C₃×C₄	—	10	2	no	—
355	C₂×C₃×C₄	—	10	2	no	—
356	C₂×C₃×C₄	—	20	4	no	—
357	C₂×C₃×C₄	—	20	4	no	—
358	C₂×C₃×C₄	D₄×D₅	1	1	yes	characteristic
359	C₂×C₃×C₄	D₄×D₅	1	1	yes	characteristic
360	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
361	C₃×C₈	—	2	1	no	—
362	C₃×C₈	—	5	2	no	—
363	C₃×C₈	—	10	1	no	—
364	C₃×C₈	C₂×C₄×D₅	1	2	yes	—
365	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
366	C₂×D₅	—	2	1	no	—
367	C₂×D₅	—	2	1	no	—
368	C₂×D₅	—	2	4	no	—
369	C₂×D₅	—	4	2	no	—
370	C₂×D₅	—	4	2	no	—
371	C₂×D₅	C₃×C₄×D₄	1	2	yes	—
372	C₄×C₅	—	2	1	no	—
373	C₄×C₅	—	2	4	no	—
374	C₄×C₅	—	4	2	no	—
375	C₄×C₅	C₃×#135	1	2	yes	complemented
376	C₄×C₅	C₂³×C₃×C₄	1	1	yes	characteristic
377	C₄×C₅	C₂×C₃×#41	1	1	yes	characteristic
378	Dic₅	—	2	1	no	—
379	Dic₅	—	4	2	no	—
380	Dic₅	C₃×C₄×D₄	1	2	yes	—
381	Dic₅	C₃×#135	1	2	yes	complemented
382	#41	—	5	8	no	—
383	#41	—	10	4	no	—
384	C₂×Q₈	C₂²×C₃×D₅	1	2	yes	—
385	C₂×D₄	—	5	2	no	—
386	C₂×D₄	—	10	2	no	—
387	C₂²×C₄	—	5	1	no	—
388	C₂²×C₄	—	5	1	no	—
389	C₂²×C₄	—	5	1	no	—
390	C₂²×C₄	—	10	2	no	—
391	C₂²×C₄	—	10	2	no	—
392	C₂²×C₄	—	10	2	no	—
393	Q₁₆	C₃×C₄×D₅	1	4	yes	complemented
394	SD₁₆	—	5	8	no	—
395	D₈	—	5	4	no	—
396	C₂×C₈	—	5	1	no	—
397	C₂×C₈	—	5	4	no	—
398	C₂×C₈	—	5	1	no	—
399	C₂×C₈	—	10	2	no	—
400	C₂×C₈	C₂²×C₃×D₅	1	1	yes	characteristic
401	C₂×C₈	C₂²×C₃×D₅	1	1	yes	characteristic
402	C₄⋊C₄	—	2	2	no	—
403	C₄⋊C₄	—	5	2	no	—
404	C₄⋊C₄	—	10	2	no	—
405	C₄⋊C₄	C₂²×C₃×D₅	1	2	yes	—
406	C₂²⋊C₄	—	10	2	no	—
407	C₂²⋊C₄	—	10	2	no	—
408	C₂²⋊C₄	—	10	2	no	—
409	C₄²	—	2	2	no	—
410	C₄²	—	5	1	no	—
411	C₄²	—	5	1	no	—
412	C₄²	—	5	1	no	—
413	C₄²	—	10	2	no	—
414	C₄²	—	10	2	no	—
415	C₄²	C₂²×C₃×D₅	1	1	yes	characteristic
416	C₃×C₅	C₄×#135	1	1	yes	characteristic, complemented, Hall
417	C₂²×C₃	—	5	2	no	—
418	C₂²×C₃	—	10	1	no	—
419	C₂²×C₃	—	10	1	no	—
420	C₂²×C₃	—	10	4	no	—
421	C₂²×C₃	—	20	2	no	—
422	C₂²×C₃	—	20	2	no	—
423	C₂²×C₃	C₂×D₄×D₅	1	1	yes	characteristic
424	C₃×C₄	—	2	1	no	—
425	C₃×C₄	—	2	4	no	—
426	C₃×C₄	—	4	2	no	—
427	C₃×C₄	—	5	2	no	—
428	C₃×C₄	—	5	2	no	—
429	C₃×C₄	—	10	1	no	—
430	C₃×C₄	—	20	2	no	—
431	C₃×C₄	#4065	1	2	yes	direct product factor
432	C₃×C₄	C₂²×C₄×D₅	1	1	yes	characteristic
433	C₃×C₄	D₅×#41	1	1	yes	characteristic
434	C₂×C₅	C₂×C₃×C₄×D₄	1	1	yes	characteristic
435	C₂×C₅	C₂×C₃×#135	1	1	yes	characteristic
436	C₂×C₅	C₂×C₃×#135	1	1	yes	characteristic
437	D₅	—	2	2	no	—
438	D₅	—	4	4	no	—
439	C₂³	—	5	1	no	—
440	C₂³	—	10	2	no	—
441	Q₈	—	2	2	no	—
442	Q₈	C₂×C₃×C₄×D₅	1	4	yes	—
443	D₄	—	5	4	no	—
444	D₄	—	10	8	no	—
445	D₄	—	10	2	no	—
446	C₂×C₄	—	2	2	no	—
447	C₂×C₄	—	2	2	no	—
448	C₂×C₄	—	5	1	no	—
449	C₂×C₄	—	5	1	no	—
450	C₂×C₄	—	5	2	no	—
451	C₂×C₄	—	5	2	no	—
452	C₂×C₄	—	5	1	no	—
453	C₂×C₄	—	10	2	no	—
454	C₂×C₄	—	10	8	no	—
455	C₂×C₄	—	10	2	no	—
456	C₂×C₄	—	10	2	no	—
457	C₂×C₄	—	20	4	no	—
458	C₂×C₄	—	20	4	no	—
459	C₂×C₄	C₃×D₄×D₅	1	1	yes	characteristic
460	C₂×C₄	C₃×D₄×D₅	1	1	yes	characteristic
461	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
462	C₈	—	2	1	no	—
463	C₈	—	5	2	no	—
464	C₈	—	10	1	no	—
465	C₈	C₂×C₃×C₄×D₅	1	2	yes	—
466	C₂×C₃	—	10	2	no	—
467	C₂×C₃	—	20	4	no	—
468	C₂×C₃	C₄×D₄×D₅	1	1	yes	characteristic
469	C₂×C₃	C₂×#4065	1	1	yes	characteristic
470	C₂×C₃	D₅×#135	1	1	yes	characteristic
471	C₅	C₃×C₄×#135	1	1	yes	characteristic, complemented, Sylow
472	C₂²	—	5	2	no	—
473	C₂²	—	10	1	no	—
474	C₂²	—	10	1	no	—
475	C₂²	—	10	4	no	—
476	C₂²	—	20	2	no	—
477	C₂²	—	20	2	no	—
478	C₂²	C₂×C₃×D₄×D₅	1	1	yes	characteristic
479	C₄	—	2	1	no	—
480	C₄	—	2	4	no	—
481	C₄	—	4	2	no	—
482	C₄	—	5	2	no	—
483	C₄	—	5	2	no	—
484	C₄	—	10	1	no	—
485	C₄	—	20	2	no	—
486	C₄	C₃×#4065	1	2	yes	direct product factor
487	C₄	C₂²×C₃×C₄×D₅	1	1	yes	characteristic
488	C₄	C₃×D₅×#41	1	1	yes	characteristic
489	C₃	C₄×#4065	1	1	yes	characteristic, direct product factor, Sylow
490	C₂	—	10	2	no	—
491	C₂	—	20	4	no	—
492	C₂	C₃×C₄×D₄×D₅	1	1	yes	characteristic
493	C₂	C₂×C₃×#4065	1	1	yes	characteristic
494	C₂	C₃×D₅×#135	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃×C₄	D₄×D₅
commutator	C₄×C₅	C₂³×C₃×C₄
Frattini	C₂×C₄	C₂³×C₃×D₅
Fitting	C₃×C₄×C₅×Q₁₆	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
prime radical	C₂×C₃×#4065	C₂
cosocle	C₂×C₄×C₅	C₂⁴×C₃
hypercenter	C₃×C₄×Q₁₆	D₅
hypocenter	C₅	C₃×C₄×#135
LCS	G ▷ C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₃×C₄ ◁ C₃×C₄² ◁ C₃×C₄×Q₁₆

Complements

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

N	H ≅ G/N	type
2. C₃×C₄×#713	C₂	semidirect
3. C₃×C₄×C₅×Q₁₆	C₂	semidirect
4. C₃×Q₁₆×Dic₅	C₂	semidirect
5. C₃×C₄×#688	C₂	semidirect
6. C₃×#65169	C₂	semidirect
7. C₃×#65161	C₂	semidirect
8. C₃×#65093	C₂	semidirect
9. C₃×#65077	C₂	semidirect
10. C₃×C₄×D₄₀	C₂	semidirect
11. C₃×C₄×C₈×D₅	C₂	semidirect
12. C₄×#4065	C₃	direct (N × H)
18. C₃×#4065	C₄	direct (N × H)
43. C₄×#713	C₂×C₃	semidirect
44. C₄×C₅×Q₁₆	C₂×C₃	semidirect
45. Q₁₆×Dic₅	C₂×C₃	semidirect
46. C₄×#688	C₂×C₃	semidirect
47. #65169	C₂×C₃	semidirect
48. #65161	C₂×C₃	semidirect
49. #65093	C₂×C₃	semidirect
50. #65077	C₂×C₃	semidirect
51. C₄×D₄₀	C₂×C₃	semidirect
52. C₄×C₈×D₅	C₂×C₃	semidirect
55. C₃×#713	C₂×C₄	semidirect
64. C₃×C₅×Q₁₆	C₂×C₄	semidirect
71. C₃×#688	C₂×C₄	semidirect
84. C₃×D₄₀	C₂×C₄	semidirect
86. C₃×C₈×D₅	C₂×C₄	semidirect
90. C₃×C₄×Q₁₆	D₅	semidirect
103. #4065	C₃×C₄	direct (N × H)
184. #713	C₂×C₃×C₄	semidirect
193. C₅×Q₁₆	C₂×C₃×C₄	semidirect
200. #688	C₂×C₃×C₄	semidirect
213. D₄₀	C₂×C₃×C₄	semidirect
215. C₈×D₅	C₂×C₃×C₄	semidirect
219. C₄×Q₁₆	C₃×D₅	semidirect
237. C₃×C₄×C₅	#135	semidirect
243. C₃×Dic₅	#135	semidirect
255. C₃×Q₁₆	C₄×D₅	semidirect
375. C₄×C₅	C₃×#135	semidirect
381. Dic₅	C₃×#135	semidirect
393. Q₁₆	C₃×C₄×D₅	semidirect
416. C₃×C₅	C₄×#135	semidirect
431. C₃×C₄	#4065	direct (N × H)
471. C₅	C₃×C₄×#135	semidirect
486. C₄	C₃×#4065	direct (N × H)
489. C₃	C₄×#4065	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×#4065	2
C₃×C₄×#713	2
C₃×C₄×C₅×Q₁₆	2
C₃×Q₁₆×Dic₅	2
C₃×C₄×#688	2
C₃×#65169	2
C₃×#65161	2
C₃×#65093	2
C₃×#65077	2
C₃×C₄×D₄₀	2
C₃×C₄×C₈×D₅	2
C₄×#4065	3
C₃×C₄×#135	5

Subgroups — C3×C4×#4065 #14416216

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₄×#4065 #14416216